Question

If one angle of a triangle is equal to the sum of other two, then the measure of that angle is ______.

Answer 1

If one angle of a triangle is equal to the sum of other two, then the measure of that angle is 90°.

Explanation:

Let the angles of a triangle be a, b and c.

It is given that,

a = b + c

We also know that,

a + b + c = 180°  ...[Angle sum property of a triangle]

⇒ a + a = 180°  ...[∵ b + c = a]

⇒ 2a = 180°

⇒ a = `180^circ/2`

⇒ a = 90°

Hence, the measure of that angle is 90°.