Question

In DEF, ∠D⩭∠F. The measure of ∠Dis nine more than nine times a number. The measure of ∠F is twelve less than twelve times the number. Find the measures of ∠D, ∠E, and ∠F

Answer 1

The value of the angles

∠ E = 36 degrees

∠ D = ∠ F = 72 degrees

How to find the angles

According to the information provided

Let the number be x

• ∠D ⩭ ∠F

The measure of ∠ Dis nine more than nine times a number.

• ∠ D = 9 + 9x

The measure of ∠F is twelve less than twelve times the number.

• ∠ F = 12x - 12

This give rise to the equation

9 + 9x = 12x - 12

9 + 12 = 12x - 9x

21 = 3x

x = 7

∠ D = 9 + 9x = 9 + 9 * 7 = 72

Sum of the angles in a triangle

∠ D + ∠ E + ∠ F = 180

72 + 72 + ∠ E = 180

∠ E = 180 - 72 - 72

∠ E = 36