Have a query? Ask a Tutor!!

Access to best educators and exclusive paper discussions

Can’t find what you’re looking for?

Our tutors are from top schools around the world, and they are waiting for you 24/7, anytime, anywhere.

Homework- One to One Solutions
Understand concepts to solve better
Get your doubts solved instantly

Maths-

General

Easy

Question

In Triangle ABC , AB= AC, and D is a point on AB. Such that AD=DC=BC. Show that $straight angle B A C equals 36 to the power of ring operator$

hint Hint:

Use the property of isosceles triangle.

The correct answer is: 36°

In ΔABC, we have
CD = BC (given)
Let $straight angle D B C equals straight angle B D C equals x to the power of ring operator$ (since angles opposite to the equal sides are always equal)
Since AB = AC, $straight angle A B C equals straight angle A C B equals x to the power of ring operator$
In ΔABC,
$straight angle A B C plus straight angle A C B plus straight angle B A C equals 180 to the power of ring operator$ (By angle sum property of the triangle)
$table attributes columnspacing 1em end attributes row cell straight angle B A C plus x plus x equals 180 to the power of ring operator end cell row cell straight angle B A C equals 180 to the power of ring operator minus 2 x end cell end table$
Since AD = CD (given),
$straight angle A C D equals straight angle D A C$
So, $straight angle D A C equals 180 to the power of ring operator minus 2 x$
Now, $straight angle B C D equals straight angle A C B minus straight angle A C D equals x minus open parentheses 180 to the power of ring operator minus 2 x close parentheses equals 3 x minus 180 to the power of ring operator$
$straight angle B D C plus straight angle D B C plus straight angle B C D equals 180 to the power of ring operator$ (angle sum property)
$x plus x plus 3 x minus 180 equals 180 to the power of ring operator$
$table attributes columnspacing 1em end attributes row cell not stretchy rightwards double arrow 5 x equals 360 to the power of ring operator end cell row cell not stretchy rightwards double arrow x equals 72 to the power of ring operator end cell end table$
Now, $straight angle B A C equals 180 minus 2 x equals 180 minus 2 left parenthesis 72 right parenthesis equals 36 to the power of ring operator$ .

Related Questions to study

In the triangle ABC, the angles at A and C are 40° and 95° respectively. If N is the foot of the perpendicular from C to AB , prove that CN = BN.

In the triangle ABC, the angles at A and C are 40° and 95° respectively. If N is the foot of the perpendicular from C to AB , prove that CN = BN.

Given XYZ is a triangle in which XW is the bisector of the angle x and XW ⊥ yz. Prove that xy= xz.

Given XYZ is a triangle in which XW is the bisector of the angle x and XW ⊥ yz. Prove that xy= xz.

ABC is a triangle in which altitudes BE and CF to sides AC and AB respectively are equal. Show that
(i) ΔABE ⩭ ΔACF
(ii) AB = AC

ABC is a triangle in which altitudes BE and CF to sides AC and AB respectively are equal. Show that
(i) ΔABE ⩭ ΔACF
(ii) AB = AC

parallel

In the figure, OA = OD and OB = OC. Show that:
(i) AOB ⩭ DOC
(ii) AB || CD

In the figure, OA = OD and OB = OC. Show that:
(i) AOB ⩭ DOC
(ii) AB || CD

If AD ⟂ CD and BC ⟂ CD , AQ = PB and DP = CQ. Prove that $straight angle D A Q equals straight angle C B P$

If AD ⟂ CD and BC ⟂ CD , AQ = PB and DP = CQ. Prove that $straight angle D A Q equals straight angle C B P$

Prove that the medians bisecting the equal sides of an isosceles triangle are also equal. If OA = OB and OD = OC, show that:
(i) AOD ⩭ BOC
(ii) AD || BC

Prove that the medians bisecting the equal sides of an isosceles triangle are also equal. If OA = OB and OD = OC, show that:
(i) AOD ⩭ BOC
(ii) AD || BC

parallel

Kumar wants to spread a carpet on the floor of his classroom. The floor is a square
with an area of 4160.25 square feet. What is the length of carpet on each side?

Kumar wants to spread a carpet on the floor of his classroom. The floor is a square
with an area of 4160.25 square feet. What is the length of carpet on each side?

The volume of a cubical box is 12167 cm³. Find the side of the box and its 6 sides area?

The volume of a cubical box is 12167 cm³. Find the side of the box and its 6 sides area?

The area of a square is 289 m², find its perimeter?

The area of a square is 289 m², find its perimeter?

parallel

What is the least seven digits which is a perfect square. Also find the square root of the number so obtained

What is the least seven digits which is a perfect square. Also find the square root of the number so obtained

Find the least number which must be subtracted from 23416 to make it a perfect square.

Find the least number which must be subtracted from 23416 to make it a perfect square.

Find the least number which must be added to 732733 to obtain a perfect square.

Find the least number which must be added to 732733 to obtain a perfect square.

parallel

In the given figure, PQ || RS. Check whether ΔPOQ i congruent to ΔSOR Give reason for your answer:

In the given figure, PQ || RS. Check whether ΔPOQ i congruent to ΔSOR Give reason for your answer:

Show that 64 is square as well as cube number

Show that 64 is square as well as cube number

From the given figures, find by which criteria the two triangles ABC and PQR are congruent.
In the figure XY = PZ. Prove that XZ = PY.
In the figure XY = PZ. Prove that XZ = PY.

From the given figures, find by which criteria the two triangles ABC and PQR are congruent.
In the figure XY = PZ. Prove that XZ = PY.
In the figure XY = PZ. Prove that XZ = PY.

parallel

card img

With Turito Academy.

card img

With Turito Foundation.

card img

Get an Expert Advice From Turito.

Turito Academy

card img

With Turito Academy.

Test Prep

card img

With Turito Foundation.