Question

using the triangle sum theorem, solve for b. using the exterior angle theorem, solve for a. 55° a° b° 65° a= b=

Explanation:

Step1: Use Triangle - Sum Theorem for b

The sum of interior angles of a triangle is 180°. So, \(55^{\circ}+65^{\circ}+b = 180^{\circ}\).
\[b=180-(55 + 65)\]
\[b = 180 - 120\]
\[b = 60^{\circ}\]

Step2: Use Exterior - Angle Theorem for a

The exterior - angle of a triangle is equal to the sum of the two non - adjacent interior angles. So, \(a=55^{\circ}+65^{\circ}\).
\[a = 120^{\circ}\]

Answer:

a = 120
b = 60