Question

ABC is a right angled triangle in which angleB =90° and AB= BC. Find angle A and angleC​

Answer 1

Answer:

The angles are ∠A = 45° and ∠C = 45°.

Step-by-step explanation:

Given:

∆ABC is a right angled triangle.

∠B = 90°

AB = BC

To find:

Values of ∠A and ∠C

Solution:

As two sides are equal, it is an Isosceles triangle.

According to isosceles triangle theorem, angles opposite to equal sides are equal.

So,

• ∠B = 90°
• ∠A = x°
• ∠C = x°

According to the angle sum property of triangle, sum of all angles in a triangle is 180°.

⇒ 90° + x° + x° = 180°

⇒ 90° + 2x = 180°

⇒ 2x = 180° - 90°

⇒ 2x = 90°

⇒ x = 90/2

⇒ x = 45°

∠A = 45° ; ∠B = 90° ; ∠C = 45°

Therefore, the angles are ∠A = 45° and ∠C = 45°.

Answer 2

Given Data :-

• ∆ABC is a right angled triangle
• ∠B = 90°
• AB = BC

To find :-

values of

• ∠A
• ∠C

Solution :-

✏ As the two given sides are equal in the triangle , It is an Isosceles triangle .

✏ According to a Isosceles triangle theorem angles opposite to equal sides are equal .

so , from the Question Data

∠A = x° = ∠C

∠B = 90°

▫As According to the Sum of angles property of triangle sum of all angles in a triangle is 180° .

⇒ x + x + 90° = 180°

⇒ 2x = 180° - 90° = 90°

⇒ x = 45°

then ,

∠A = 45°

and ∠C = 45°