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Lapatulllka [165]
2 years ago
14

Suppose ΔDEF has an exterior angle at vertex D. The measure of the exterior angle is (8x−2)º, m∠E=(3x−8)°, and m∠F=(4x+13)°. Wha

t is the measure of the exterior angle at vertex D?
A. 7°
B. 13°
C. 41°
D. 54°
Mathematics
1 answer:
miv72 [106K]2 years ago
7 0

The measure of the exterior angle at vertex D is: D. 54°

<em><u>Recall:</u></em>

  • The exterior angle theorem of a triangle states that the measure of an exterior angle equals the sum of the measures of two opposite interior angles of the triangle.

<em><u>Thus:</u></em>

In ΔDEF, (8x−2)º is an exterior angle at vertex D.

m∠E = (3x−8)° (interior angle)

m∠F = (4x+13)° (interior angle)

<em>Therefore:</em>

(8x−2)º = (3x−8)° + (4x+13)°

  • Solve for x

8x - 2 = 3x - 8 + 4x + 13

  • Combine like terms

8x - 2 = 7x + 5

8x - 7x = 2 + 5

x = 7

Exterior angle at vertex D = (8x−2)º

  • Plug in the value of x

= 8(7) - 2

= 54º (option D)

Learn more about exterior angle theorem on:

brainly.com/question/24756010

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