Answer:
d. 102°
Explanation:
We can use the relations ...
- corresponding angles in congruent triangles are congruent
- the sum of angles in a triangle is 180°
to write equations that let us find x and all of the angles in ∆PQR.
Corresponding angles
The congruence relation ∆ABC ≅ ∆PQR tells us that ∠P = ∠A. Using the given expressions for these angles, we have ...
∠P = ∠A
8x +4 = 5x +16
3x = 12 . . . . . . . . . subtract (5x+4)
x = 4 . . . . . . . . . divide by 3
Then the measure of angle P is ...
∠P = 8x +4 = 8(4) +4 = 36 . . . . . degrees
Other angles
Angle Q in ∆PQR is given as ...
∠Q = 10x +2 = 10(4) +2 = 42 . . . . . degrees
Then the measure of angle R needed to make the total of angles in ∆PQR be 180° is ...
∠R = 180° -36° -42° = 102°
Angle R is 102°.
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In summary:
- x = 4
- ∠P = ∠A = 36°
- ∠Q = ∠B = 42°
- ∠R = ∠C = 102°