Maths-

General

Easy

Question

# Intersecting lines r, s and t are shown below .

Hint:

**Hint:-** The exterior angle theorem states that when a triangle's side is extended, the resultant exterior angle formed is equal to the sum of the measures of the two opposite interior angles of the triangle.

## The correct answer is: x = 97°

### Solution:

Supplementary angles are those angles that sum up to 180 degrees.

- Let us first name the points of intersection.

- For solving further we will consider the triangle ABC.
- Given:-

External angle A with line s= 106°

Angle B of triangle ABC = 23°

External angle C with line r= x°

- We will first find the angle CAB , as it is supplementary angle to external angle A with line s ,
- Angle CAB + External angle A with line s= 180°

Angle CAB + 106° = 180°

Therefore,

Angle CAB = 180°- 106°

Angle CAB = 74°

- Angle x° is exterior angle of triangle ABC,

Angle CAB + Angle ABC = Angle x°

74° + 23° = x°

- Therefore x = 97°

### Related Questions to study

Maths-

### The surface area of a cube is 6(a/4)^{2},where *a *is a positive constant. Which of the following gives the perimeter of one face of the cube?

### The surface area of a cube is 6(a/4)^{2},where *a *is a positive constant. Which of the following gives the perimeter of one face of the cube?

Maths-General

Maths-

If (x, y) is a solution of the system of equations above and x > 0, what is the value of xy ?

If (x, y) is a solution of the system of equations above and x > 0, what is the value of xy ?

Maths-General

Maths-

In triangle *ABC *above, side AC is extended to

point *D*. What is the value of *y-x*?

**Note: **

It is important to know the basic properties of a triangle to solve such problems. The most important property to remember is; the sum the interior angles of a triangle is 180°. This is often used in solving problems in geometry.

In triangle *ABC *above, side AC is extended to

point *D*. What is the value of *y-x*?

Maths-General

**Note: **

It is important to know the basic properties of a triangle to solve such problems. The most important property to remember is; the sum the interior angles of a triangle is 180°. This is often used in solving problems in geometry.

Maths-

### A psychologist set up an experiment to study the tendency of a person to select the first item when presented with a series of items. In the experiment, 300 people were presented with a set of five pictures arranged in random order. Each person was asked to choose the most appealing picture. Of the first 150 participants, 36 chose the first picture in the set. Among the remaining 150 participants, *p *people chose the first picture in the set. If more than 20% of all participants chose the first picture in the set, which of the following inequalities best describes the possible values of *p *?

### A psychologist set up an experiment to study the tendency of a person to select the first item when presented with a series of items. In the experiment, 300 people were presented with a set of five pictures arranged in random order. Each person was asked to choose the most appealing picture. Of the first 150 participants, 36 chose the first picture in the set. Among the remaining 150 participants, *p *people chose the first picture in the set. If more than 20% of all participants chose the first picture in the set, which of the following inequalities best describes the possible values of *p *?

Maths-General

Maths-

### In air, the speed of sound *S*, in meters per second, is a linear function of the air temperature *T*, in degrees Celsius, and is given by *S(T) *= 0.6*T* + 331.4. Which of the following statements is the best interpretation of the number 331.4 in this context?

### In air, the speed of sound *S*, in meters per second, is a linear function of the air temperature *T*, in degrees Celsius, and is given by *S(T) *= 0.6*T* + 331.4. Which of the following statements is the best interpretation of the number 331.4 in this context?

Maths-General

Maths-

### Jackie has two summer jobs. She works as a tutor, which pays $12 per hour, and she works as a lifeguard, which pays $9.50 per hour. She can work no more than 20 hours per week, but she wants to earn at least $220 per week. Which of the following systems of inequalities represents this situation in terms of *x *and *y*, where *x *is the number of hours she tutors and *y *is the number of hours she works as a lifeguard?

### Jackie has two summer jobs. She works as a tutor, which pays $12 per hour, and she works as a lifeguard, which pays $9.50 per hour. She can work no more than 20 hours per week, but she wants to earn at least $220 per week. Which of the following systems of inequalities represents this situation in terms of *x *and *y*, where *x *is the number of hours she tutors and *y *is the number of hours she works as a lifeguard?

Maths-General

Maths-

The Townsend Realty Group invested in the five different properties listed in the table above. The table shows the amount, in dollars, the company paid for each property and the corresponding monthly rental price, in dollars, the company charges for the property at each of the five locations.

Townsend Realty purchased the Glenview Street property and received a 40% discount off the original price along with an additional 20% off the discounted price for purchasing the property in cash. Which of the following best approximates the original price, in dollars, of the Glenview Street property?

The Townsend Realty Group invested in the five different properties listed in the table above. The table shows the amount, in dollars, the company paid for each property and the corresponding monthly rental price, in dollars, the company charges for the property at each of the five locations.

Townsend Realty purchased the Glenview Street property and received a 40% discount off the original price along with an additional 20% off the discounted price for purchasing the property in cash. Which of the following best approximates the original price, in dollars, of the Glenview Street property?

Maths-General

Maths-

The Townsend Realty Group invested in the five different properties listed in the table above. The table shows the amount, in dollars, the company paid for each property and the corresponding monthly rental price, in dollars, the company charges for the property at each of the five locations.

The relationship between the monthly rental price *r*, in dollars, and the property’s purchase price *p*, in thousands of dollars, can be represented by a linear function. Which of the following functions represents the relationship?

The Townsend Realty Group invested in the five different properties listed in the table above. The table shows the amount, in dollars, the company paid for each property and the corresponding monthly rental price, in dollars, the company charges for the property at each of the five locations.

The relationship between the monthly rental price *r*, in dollars, and the property’s purchase price *p*, in thousands of dollars, can be represented by a linear function. Which of the following functions represents the relationship?

Maths-General

Maths-

In a survey, 607 general surgeons and orthopedic surgeons indicated their major professional activity. The results are summarized in the table above. If one

of the surgeons is selected at random, which of the following is closest to the probability that the selected surgeon is an orthopedic surgeon whose indicated

professional activity is research?

In a survey, 607 general surgeons and orthopedic surgeons indicated their major professional activity. The results are summarized in the table above. If one

of the surgeons is selected at random, which of the following is closest to the probability that the selected surgeon is an orthopedic surgeon whose indicated

professional activity is research?

Maths-General

Maths-

The system of equations above has solution *(x, y). *What is the value of *x *?

The system of equations above has solution *(x, y). *What is the value of *x *?

Maths-General

Maths-

### In State X, Mr. Camp’s eighth-grade class consisting of 26 students was surveyed and 34.6 percent of the students reported that they had at least two siblings. The average eighth‑grade class size in the state is 26. If the students in Mr. Camp’s class are representative of students in the state’s eighth-grade classes and there are 1,800 eighth-grade classes in the state, which of the following best estimates the number of eighth‑grade students in the state who have fewer than two siblings?

### In State X, Mr. Camp’s eighth-grade class consisting of 26 students was surveyed and 34.6 percent of the students reported that they had at least two siblings. The average eighth‑grade class size in the state is 26. If the students in Mr. Camp’s class are representative of students in the state’s eighth-grade classes and there are 1,800 eighth-grade classes in the state, which of the following best estimates the number of eighth‑grade students in the state who have fewer than two siblings?

Maths-General

Maths-

### Which of the following is equivalent to the sum of the expressions a^{2} - 1 and a + 1 ?

### Which of the following is equivalent to the sum of the expressions a^{2} - 1 and a + 1 ?

Maths-General

Maths-

### Horsepower and watts are units of measure of power. They are directly proportional such that 5 horsepower is equal to 3730 watts. How much power, in watts, is equal to 2 horsepower?

### Horsepower and watts are units of measure of power. They are directly proportional such that 5 horsepower is equal to 3730 watts. How much power, in watts, is equal to 2 horsepower?

Maths-General

Maths-

### 2(p + 1) + 8(p - 1) = 5p

What value of *p *is the solution of the equation above?

### 2(p + 1) + 8(p - 1) = 5p

What value of *p *is the solution of the equation above?

Maths-General

Maths-

In the equation above, if a is negative and b is positive, which of the following must be true?

In the equation above, if a is negative and b is positive, which of the following must be true?

Maths-General