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3 years ago

50 POINTS!!!!! Consider the picture below. Find the measure of ∠A

Mathematics

1 answer:

True [87]3 years ago

4 0

Answer:

103°

Step-by-step explanation:

∠CEA and ∠DEB are vertically opposite angles same as ∠CED and ∠AEB.

Vertically opposite angles are angles that form when two lines intersect

From the figure given, lines CB and AD intersect to form vertically opposite angles mentioned above. Vertically opposite angles are equal, meaning

∠CEA=∠DEB and ∠CED=∠AEB

Replacing ∠CED=∠AEB, we get

(14x+7)°=(12x+17)°

Solve for x

(14x-12x)=17-7

2x=10

x=10÷2=5

value for x in ∠CED=∠AEB, we get (14×5)+7=77°

To calculate ∠CEA and ∠DEB

Let ∠CEA=∠DEB=y

∠DEA=180°since its a straight line therefor

(14x+7)°+y=180°

77+y=180

y=∠CEA=∠DEB=103°

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