The values of x and y are 8.6 and 17, respectively, and the measure of ∠DFE is 88°.
Here's what I see in the diagram:
Parallel lines: Two parallel lines are intersected by a transversal.
Angle measures: The following angle measures are given:
- (5x - 7)°
- 36°
- (5y + 3)°
- 92°
∠DFE: This angle is located on the transversal and is adjacent to a given angle.
Steps to find x, y, and ∠DFE:
1. Identify corresponding angles:
∠DFE and the angle labeled (5y + 3)° are corresponding angles because they are on the same side of the transversal and in corresponding positions relative to the parallel lines. Corresponding angles are equal when lines are parallel.
2. Set up an equation: Based on the corresponding angles, we can set up the equation: ∠DFE = (5y + 3)°
3. Find y:
- The angle adjacent to ∠DFE is given as 92°.
- Together, these two angles form a straight line (180°).
- Therefore, we can set up the equation:
∠DFE + 92° = 180°
- Substitute (5y + 3)° for ∠DFE:
(5y + 3)° + 92° = 180°
- Solve for y:
5y = 85
y = 17
4. Find x: The angle labeled (5x - 7)° is vertically opposite to the angle labeled 36°.
- Vertically opposite angles are equal.
- Therefore, we can set up the equation:
5x - 7 = 36
- Solve for x:
5x = 43
x = 8.6
5. Find ∠DFE: Substitute the value of y into the equation for ∠DFE:
∠DFE = (5y + 3)°
∠DFE = (5 * 17 + 3)°
∠DFE = 88°
Complete the question:
Find the values of x and y. then find the measure of ∠ DFE.