342,491 views
30 votes
30 votes
Triangle abc is equal to

triangle pqr, angle p=8X+4,
angle a=5x+16 , and angle
q=10x+2. find angle r
a. 36
b.not enough info
c. 42
d 102

User Mejobloggs
by
2.9k points

1 Answer

26 votes
26 votes

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°.

__

In summary:

  • x = 4
  • ∠P = ∠A = 36°
  • ∠Q = ∠B = 42°
  • ∠R = ∠C = 102°
User Vivek Parmar
by
2.3k points