Answer:
m∠QTP = 43°
Step-by-step explanation:
As with any problem, you start by looking at what you are given and the relationships between those things and what you are to find.
There are several relationships you can make use of here:
- the sum of angles of a triangle is 180°
- vertical angles are congruent
- corresponding angles are congruent where a transversal crosses parallel lines
The angles marked (3x°) and (5x-32)° are corresponding angles, so are congruent. That means you can find their measure:
3x = 5x -32
0 = 2x -32 . . . . . subtract 3x
0 = x -16 . . . . . . . divide by 2
16 = x . . . . . . . . . .add 16
3x° = 48° . . . . . . find 3x°
Angle TPQ is vertical with 3x°, so also has measure 48°. Angle TQP is vertical with the angle marked 89°, so also has measure 89°.
Now, you know two of the three angles in triangle QTP, so you can find angle QTP:
m∠QTP + 48° + 89° = 180° . . . sum of angles in a triangle
m∠QTP = 43° . . . . . . . . . . . . . . subtract 137°
