Each corner of a triangle can form an exterior angle of the triangle by extending one side of the triangle. As we can see in above picture, where 'w' is exterior angle of angle 'z'.
The measure of the exterior angle to ∠d is 126°. So, the correct option is option (D).
We have given that,
A ∆DEF such that m∠d = (2x + 19)°,
m∠e = (3x + 24)°, and m∠f = 87°.
we have to find out the degree measure of the exterior angle to ∠d.
As we know that sum of angles of triangle is equal to 180° .
so, m∠d + m∠e + m∠f = 180°
=> (3x + 24)° + (2x + 19)° + 87° = 180°
=> (5x + 24 + 19 + 87)° = 180°
=> 5x + 130° = 180°
=> 5x = 50°
=> x = 10°
plug this value in angle d , angle e we get ,
m∠d = (3 ×10 + 24 )° = 54°
We can see that adding the angle measurement d and the exterior angle measurement gives d = 180 degrees. This is because they are a pair of adjacent angles and both lie on a straight line.
measure of Exterior angle of ∠d + measure of ∠d = 180°
Measure of exterior angle of ∠d
= 180° - m∠d
= 180° - 54° = 126°
Hence, the measure of exterior angle of d is 126°.
To learn more about exterior angle, refer:
https://brainly.com/question/29125448
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