Two angles, ∠1 and ∠2 in a diagram are complementary. If m∠2 = 26°, what equation can you write to solve for m∠1?

Answer 1

The sum of two complementary angles is 90 degrees.

Let m∠1 be the measure of angle ∠1.

Since ∠1 and ∠2 are complementary, we have m∠1 + m∠2 = 90.

Substituting m∠2 = 26° into the equation, we get:

m∠1 + 26 = 90

So the equation to solve for m∠1 is m∠1 + 26 = 90.

Answer 2

In a diagram, ∠3 and ∠5 are vertical angles, and ∠4 is a supplementary angle with ∠5. If m∠3 = 67°, what equation can you write to solve m∠4?

Answer 3

Vertical angles are always congruent, meaning they have the same measure.

Let m∠3 be the measure of angle ∠3, m∠4 be the measure of angle ∠4, and m∠5 be the measure of angle ∠5.

Since ∠3 and ∠5 are vertical angles, we have m∠3 = m∠5.

Since ∠4 is a supplementary angle with ∠5, we have m∠4 + m∠5 = 180.

Substituting m∠3 = 67° into the equation m∠3 = m∠5, we get:

67 + m∠4 = 180

So the equation to solve for m∠4 is 67 + m∠4 = 180.