∠D and ∠E are complementary angles. m∠D = (3x - 1)° and m∠E = (4x + 21)°. Find m∠D.

Question

∠D and ∠E are complementary angles. m∠D = (3x - 1)° and m∠E = (4x + 21)°. Find m∠D.

Answer 1

Complementary angles have measures that add up to 90 degrees. For example, the acute angles of a right triangle are complementary.

The expressions (3x - 1) and (4x + 21) represent the measures of angles D and E respectively. That means the following equation represents the scenario:

3x -1 + 4x + 21 = 90

7x + 20 = 90

7x = 70

x = 10

That is not the answer to the question. To find the measure and angle D substitute 10 into the expression (3x - 1) for x.

3(10) - 1 = 29

For angle E:

4x + 21 = 4(10) + 21 = 61

And 29 + 61 = 90 (check)