Question

Multi-Step: For what values of the variables △QPR congruent to △SPR? In this case, what is m ∠Q?

Answer 1

• x = 17
• y = 8
• ∠Q = 85°

Explanation:

You want the values of the variables x and y, and the measure of angle Q in the given figure when ∆QPR ≅ ∆SPR.

Congruence

The triangles are congruent by the ASA postulate when the angles at P are congruent and the angles at R are congruent.

Angles at P

(2x +1)° = (x +18)°

x = 17 . . . . . . . . . . . divide by °, subtract x+1

(x +18)° = (17 +18)° = 35° . . . . the measures of the angles at P

Angles at R

(8y -4)° = (4y +28)°

4y = 32 . . . . . . . . . . . divide by °, add 4-4y

y = 8 . . . . . . . . . divide by 4

(4y +28)° = (32 +28)° = 60° . . . . . . the measures of the angles at R

Angle Q

The sum of angles in ∆QPR is 180°, so ...

Q +35° +60° = 180°

Q = 85° . . . . . . . . . . . subtract 95°

For x = 17 and y = 8, the triangles are congruent. m∠Q = 85°.

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