Answer:
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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