The degree measure of the exterior angle triangle is ∠D = 137°.
Having three vertices and three angles that add up to 180 degrees, a triangle is a three-sided polygon.
given this, the angles D, E, and F in the triangle DEF are (4x + 15), (5x + 32), and 70 respectively.
The sum of the angles of a triangle is now 180°.
Therefore, we may write: m ∠D m∠ E m ∠F = 180
When all the numbers are substituted, we obtain the following results: (9x + 117 = 180) 9x
= 180 -117 (4x + 15) + (5x + 32) + 70
⇒ 9x = 63
⇒ x = 7
As a result, we obtain m∠ D = (4x + 15)°,
m∠ D = (4 x 7 + 15)°,
m ∠D = (28 + 15)°, and m∠ D = (43)°.
Furthermore, m∠ E = (5x + 32)°
m ∠E = (5 x 7 + 32)°
m ∠E = (35 + 32)°
m ∠E = 67°
Since, The measure of the exterior angle to ∠D = m ∠E + m ∠F
= 67° + 70
= 137°
Thus, The measure of the exterior angle ∠D will be 137°.
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