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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

User Mkungla
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1 Answer

4 votes

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

In DEF, ∠D⩭∠F. The measure of ∠Dis nine more than nine times a number. The measure-example-1
User Tomek Tarczynski
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