Question

8. One of the two equal angles of an isosceles triangle measures 65°. Find the measure of each angie
of the triangle.
9. Find the measure of each of the two equal angles of an isosceles right-angled triangle.
10. If all the three angles of a triangle are of the same measure, find the measure of each of the angles
11. In a right-angled triangle if one of the acute angles measures 40°, find the measure of the other
acute angles.​

Answer 1

ANSWER

Given two equal angle of isoscles triangle

are 55

∘

Let third angle be x then

x+55+55=180

∘

[angle sum property]

x=180−110

∘

(x=70

∘

)

∴ the other angle is 70

∘

Answer 2

8. One of the two equal angles of an isosceles triangle measures 65°, Find the measure of each angles.

$\large{\boxed{\bf{Answer}}}$

65°, 65°, 50°

__________________________

Given :-

• One of the two equal angles of an isosceles triangle measures 65°

To Find :-

• Measure of each angles.

__________________________

$\large{\boxed{\bf{Solution}}}$

★ We know that base angles of an isosceles triangle are equal.

So, another equal angle will be 65°.

• Let another angle be x

then,

★ 65 + 65 + x = 180

=> 130 + x = 180

=> x = 180 - 30

=> x = 50°

Hence, the value of other angle is 50°

∴ All angles of the isosceles triangle are 65°, 65° and 50° respectively.

__________________________

9. Find the measure of each of the two equal angles of an isosceles right angled triangle.

$\large{\boxed{\bf{Answer}}}$

45°, 45°

__________________________

Given :-

• An isosceles right triangle.

To Find :-

• Measure of each of the two equal angles of the triangle.

__________________________

$\large{\boxed{\bf{Solution}}}$

★ We know that, in an isosceles right triangle two angles are equal and other angle is of 90°.

So, another angle will be 90°

• Let equal angles be x

Then,

★ x + x + 90 = 180

=> 2x + 90 = 180

=> 2x = 180 - 90

=> 2x = 90

=> x = 90/2

=> x = 45°

Hence, two equal angles of the traingle are 45° and 45° respectively.

__________________________

10. If all the three angles of the triangle are of same measure, find the measure of each of the angles.

$\large{\boxed{\bf{Answer}}}$

60°, 60°, 60°

__________________________

Given :-

• All three angles of a triangle are of same measure.

To Find :-

• Measure of each of the angles.

__________________________

$\large{\boxed{\bf{Solution}}}$

★ We know that if all angles of a triangle are equal, then it will be an equilateral triangle.

So, all angles will be of same measure and it will be an equilateral triangle.

• Let equal angles be x.

Then,

★ x + x + x = 180

=> 3x = 180

=> x = 180/3

=> x = 60°

Hence, all angles of the triangle are 60°, 60° and 60°.

__________________________

11. In a right-angled triangle if one of the acute angles measures 40°, find the measure of the other acute angles.

$\large{\boxed{\bf{Answer}}}$

50°

__________________________

Given :-

• In a right triangle, one of the acute angles measures 40°

To Find :-

• Measure of other angles.

__________________________

$\large{\boxed{\bf{Solution}}}$

★ We know that, in a right triangle there is an angle of 90°.

So, another one angle is of 90°.

Let another angle be x,

Then,

★ 40 + 90 + x = 180

=> x + 130 = 180

=> x = 180 - 130

=> x = 50°

Hence, another angle of the triangle is 50°.

__________________________