Answer:
Explanation:
You want to know the values of x and y that make the angle measures consistent with the triangles being congruent in the given figure.
Congruence
The side markings show congruent triangles with corresponding vertices (and angles) ...
L (3x+24)° ⇔ P (8x -11)°
M 84° ⇔ Q 84°
N (2x +y)° ⇔ R (no marking)
Corresponding angles L and P have the same measure, so ...
3x +24 = 8x -11
35 = 5x . . . . . . . . add 11-3x
7 = x . . . . . . . . . divide by 5
The measures of these angles are ...
(3(7) +24)° = 45°
Angle sum theorem
The sum of the angles in each triangle is 180°, so the measure of angle N is found to be ...
L +M +N = 180°
45° +84° +N = 180°
N = 51°
This lets us find the value of y from ...
(2x +y)° = 51°
2(7) +y = 51
y = 37 . . . . . . . . subtract 14
The value of x is 7. The value of y is 37.