Answer:
The measure of an exterior angle = 125°
Hence, option A is correct.
Step-by-step explanation:
As the given triangle is a right-angled triangle ΔABC.
Given the angles
We know that the sum of angles in a triangle is 180°.
Thus,
m∠A + m∠B + m∠C = 180°
substituting m∠A = 35° and m∠C = 90° in the equation
35° + m∠B + 90° = 180°
125 + m∠B = 180°
subtract 125 from both sides
125 + m∠B - 125 = 180° - 125
m∠B = 55°
Thus, the measure of angle B is:
m∠B = 55°
As the exterior angle of the given triangle is adjacent to m∠B = 55°.
We know that the exterior angle of a triangle is equal to the sum of two opposite interior angles.
Here,
∠A and ∠C are two opposite interior angles of the exterior angle.
Thus,
The measure of an exterior angle is equal to the sum of two opposite interior angles.
as
so
Exterior angle = m∠A + m∠C
= 35° + 90°
= 125°
Thus, the measure of an exterior angle = 125°
Hence, option A is correct.
