Question

in fig 10.44, ABC is triangle such that angleABC = angleACB. Find the angles of the triangle​

Answer 1

Given:

• ∠ACD = 135°
• ∠ABC = ∠ACB = x°

To find:

1. ∠BAC, ∠ACB, ∠ABC

Method:

By linear pair of Angles,

∠ACD + ∠ACB = 180°

⇒ 135° + ∠ACB = 180°

⇒ ∠ACB = 180° - 135°

⇒ ∠ACB = 45°

We know that ∠ABC = ∠ACB

∴ ∠ABC = 45°

In ΔABC,

By Angle Sum Property;

∠ABC + ∠ACB + ∠BAC = 180°

⇒ 45° + 45° + ∠BAC = 180°

⇒ 90° + ∠BAC = 180°

⇒ ∠BAC = 180° - 90°

⇒ ∠BAC = 90°

Additional Information:

• Linear pair of angles states that Sum of 2 angles on a straight line is always 180°
• Angle Sum Property states that Sum of all angles in a triangle is always 180°
• This question can be approached in another method that is by using Exterior Angle Property. This property states that Exterior Angle is equal to Sum of opposite 2 interior angles