Answer:
- (4x-9)° +(6x+2)° +x° = 180°
- ∠P = 59°
- ∠Q = 104°
- ∠R = 17°
Explanation:
Given ∆PQR with ∠P = (4x-9)°, ∠Q = (6x+2)°, and ∠R = x°, you want an equation to find x, and the measures of the angles.
Equation
The equation expresses the fact that the sum of angles in a triangle is 180°.
∠P +∠Q +∠R = 180°
(4x -9)° +(6x +2)° +x° = 180°
Solution
11x -7 = 180 . . . . . . . . . . . . divide by °, collect terms
11x = 187 . . . . . . . . . add 7
x = 17 . . . . . . . . divide by 11
Angles
The angle measures are found by substituting for x in the angle expressions:
∠P = (4·17 -9)° = 59°
∠Q = (6·17 +2)° = 104°
∠R = 17°