To solve such problems we need to know about supplementary angles.
Supplementary Angle
When the sum of two angles measures up to 180° then these angles are known as supplementary angles of each other.
for example, ∠x + ∠y = 180°, therefore, the ∠x and ∠y are the supplementary angles of each other.
The exterior angle to ∠C is ∠D, which is the supplementary angle to ∠c and also, to the sum of ∠A and ∠B.
Explanation
Given information:
A triangle has angles A, B, C. The exterior angle to angle C is angle D.
We know,
Supplementary angles are those two angles whose sum measures up to 180°.
These angles are when adjacent to each other, they form a straight line.
In ΔABC,
∠C and ∠D form a line BE.
therefore, the ∠C and ∠D are supplementary angles for each other, and
∠C + ∠D = 180°.
∠C = 180° - ∠D
Also, we know that the sum of all angles of a triangle is 180°.
So, ∠A + ∠B + ∠C = 180°
Substituting the value of ∠C,
∠A + ∠B + (180° - ∠D) = 180°
Canceling 180° from both sides,
∠A + ∠B + 180° - ∠D = 180°
∠A + ∠B - ∠D = 0
∠A + ∠B = ∠D
Hence, the exterior angle to ∠C is ∠D, which is the supplementary angle to ∠c and also, to the sum of ∠A and ∠B.
Learn more about external angles:
https://brainly.com/question/2125016
