Question

# Find x if PQ || RS and ∠1: ∠2 = 3: 5.

- 60°
- 75°
- 37.5°
- 135°

Hint:

### Find the angles of triangle OSR and apply the ratio and Angle Sum property of triangle to get the equation upon solving we get x.

## The correct answer is: 37.5°

PQ || RS ⇒ ∠PQO = ∠OSR (Alternate Interior Angles)

⇒ ∠1 = x ——— (i)

Also, ∠POQ = ∠SOR (Vertically Opposite Angles)

⇒ ∠SOR = 80°

In ∆ SOR, ∠OSR + ∠SRO + ∠ROS = 180° (Angle Sum property of triangle)

⇒ x + ∠2 + 80° = 180°

⇒ ∠1 + ∠2 = 100°

⇒ ∠1 + (5/3) ∠1 = 100° (∠1: ∠2 = 3: 5)

⇒ (8/3) ∠1 = 100°

⇒ ∠1 = 37.5°

From equation (i), x = ∠1 = 37.5°.

⇒ ∠1 = x ——— (i)

Also, ∠POQ = ∠SOR (Vertically Opposite Angles)

⇒ ∠SOR = 80°

In ∆ SOR, ∠OSR + ∠SRO + ∠ROS = 180° (Angle Sum property of triangle)

⇒ x + ∠2 + 80° = 180°

⇒ ∠1 + ∠2 = 100°

⇒ ∠1 + (5/3) ∠1 = 100° (∠1: ∠2 = 3: 5)

⇒ (8/3) ∠1 = 100°

⇒ ∠1 = 37.5°

From equation (i), x = ∠1 = 37.5°.

### Related Questions to study

### From the diagram given below, which of the following option is true?

### From the diagram given below, which of the following option is true?

### Find the angle ∠SOR if PQ || RS and ∠OSR: ∠SRO = 2: 3.

### Find the angle ∠SOR if PQ || RS and ∠OSR: ∠SRO = 2: 3.

### Find the value of x if BO and OC are angle bisectors of angle B and C respectively

### Find the value of x if BO and OC are angle bisectors of angle B and C respectively

### Which of the following relation is correct if the altitudes BD and CE are equal?

### Which of the following relation is correct if the altitudes BD and CE are equal?

### In which of the following figures do the dotted lines represent the figure's line of symmetry?

### In which of the following figures do the dotted lines represent the figure's line of symmetry?

### What is the value of ∠PQB if PQ ⊥ PB and RS ⊥ AR and RS = PQ, AP = BR?

Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure. These triangles can be slides, rotated, flipped and turned to be looked identical.

### What is the value of ∠PQB if PQ ⊥ PB and RS ⊥ AR and RS = PQ, AP = BR?

Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure. These triangles can be slides, rotated, flipped and turned to be looked identical.

Write the rule for this translation: Slide 3 up and 2 right

Write the rule for this translation: Slide 3 up and 2 right

Which of the following figures has rotational symmetry of order more that I?

Hence Both A and C is the Correct option.

Which of the following figures has rotational symmetry of order more that I?

Hence Both A and C is the Correct option.

### What is the relation between ∠1 and ∠2 if AD = CD?

### What is the relation between ∠1 and ∠2 if AD = CD?

### Identify the type of triangle if altitudes AD, BE and CF are equal.

An equilateral triangle is considered as a regular polygon or a regular triangle as angles are equal and sides are also equal.

### Identify the type of triangle if altitudes AD, BE and CF are equal.

An equilateral triangle is considered as a regular polygon or a regular triangle as angles are equal and sides are also equal.

A translation is a transformation

A translation is a transformation

### From the diagram given below, we can say that ΔABC and ΔPQR are ________.

Hence Congruennt is perfect option

### From the diagram given below, we can say that ΔABC and ΔPQR are ________.

Hence Congruennt is perfect option

Which of the following alphabets has a horizontal line of symmetry?

Hence All of These is the suitable option.

Which of the following alphabets has a horizontal line of symmetry?

Hence All of These is the suitable option.

A translation function is defined by the rule (*x, y*) → (*x* + 2, *y* - 5).

Which choice will be the image of the point (3, 6) under this translation?

In this question, we used the concept of translation and found out the points according to the condition given. We also understood the concept of the cartesian system and the coordinates. In translation, only the position of the object changes, its size remains the same. The algebraic representation will be: (5, 1).

A translation function is defined by the rule (*x, y*) → (*x* + 2, *y* - 5).

Which choice will be the image of the point (3, 6) under this translation?

In this question, we used the concept of translation and found out the points according to the condition given. We also understood the concept of the cartesian system and the coordinates. In translation, only the position of the object changes, its size remains the same. The algebraic representation will be: (5, 1).

Which of the following figures has multiple lines of symmetry (more than one line of symmetry)?

If a line can be drawn separating a figure into two identical pieces, the figure possesses line symmetry. The path is known as a symmetry line. A figure might only contain one line of symmetry, two lines of symmetry, or none at all. So here the figure 4 has more than 1 line of symmetry.

Which of the following figures has multiple lines of symmetry (more than one line of symmetry)?

If a line can be drawn separating a figure into two identical pieces, the figure possesses line symmetry. The path is known as a symmetry line. A figure might only contain one line of symmetry, two lines of symmetry, or none at all. So here the figure 4 has more than 1 line of symmetry.