Question

Find the values of x and y. Then find the measure of
x= _______
y= _______
m

Answer 1

9y = 36 therefore y=4

5x-7 = 88

5x = 95 therefore x=19

*IT IS 88 because the bottom left angle where F is the same as the 92 degrees by D. 180 - 92 = 88

Measure of DFE is 180 - 36 - 88 = 56

Answer 2

The values x = 19°: y = 4°: DFE = 56°

Finding y:

9y = 36°: This equation represents the relationship between angle B and angle D. Since alternate interior angles are equal, we have B = D = 92°.

Solving for y: Divide both sides by 9: y = 4°.

Finding x:

5x - 7 = 88°: This equation represents the relationship between angle A and angle F. Since corresponding angles are equal, we have A = F = 36°.

Solving for x: Add 7 to both sides: 5x = 95°.

Divide both sides by 5: x = 19°.

Finding LDFE:

Angle sum property: The sum of the angles in a triangle is 180°.

Apply the property: LDFE + 92° + (5x - 7) = 180°.

Substitute x value: LDFE + 92° + (5 * 19° - 7) = 180°.

Simplify and solve: LDFE + 92° + 90° = 180°. LDFE = 56°.

Therefore:

x = 19°

y = 4°

DFE = 56°