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Delicious77
14 days ago
12

[GEOMETRY] If m∠DEG= 5x - 4 m∠GEF=7x - 8 m∠DEH= 9y + 5 find the values of x and y

Mathematics
1 answer:
Zina [3.9K]14 days ago
9 0

Given:

Line DEF is straight, so the angles on it sum to 180°.

Thus, angle(DEG) + angle(GEF) = 180°.

Substitute the provided values:

5x-4+7x-8=180

12x-12=180

12x=192

x=16 — Answer

Since vertically opposite angles are equal,

angle(GEF) = angle(DEH).

Substitute in known expressions:

9y+5=7x-8

Plug in x = 16:

9y+5=7*16-8

9y+5=104

9y=99

y=11 — Final Answer

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