Question

name jenna
facts: ∠a and ∠b are complementary angles
∠b and ∠c are supplementary angles

1. if m∠a=52, then m∠b =__ and m∠c =__

2.) if m∠b=67, then m∠a=__ and m∠c=__
3.) if m∠c=107, then m∠b=__ and m∠a=__

Explanation:

Problem 1

Step1: Recall complementary angles sum to 90°

Since \( \angle A \) and \( \angle B \) are complementary, \( m\angle A + m\angle B = 90^\circ \). Given \( m\angle A = 52^\circ \), we solve for \( m\angle B \):
\( 52^\circ + m\angle B = 90^\circ \)
\( m\angle B = 90^\circ - 52^\circ = 38^\circ \)

Step2: Recall supplementary angles sum to 180°

Since \( \angle B \) and \( \angle C \) are supplementary, \( m\angle B + m\angle C = 180^\circ \). Substitute \( m\angle B = 38^\circ \):
\( 38^\circ + m\angle C = 180^\circ \)
\( m\angle C = 180^\circ - 38^\circ = 142^\circ \)

Step1: Use complementary angles for \( \angle A \) and \( \angle B \)

\( m\angle A + m\angle B = 90^\circ \). Given \( m\angle B = 67^\circ \):
\( m\angle A = 90^\circ - 67^\circ = 23^\circ \)

Step2: Use supplementary angles for \( \angle B \) and \( \angle C \)

\( m\angle B + m\angle C = 180^\circ \). Substitute \( m\angle B = 67^\circ \):
\( 67^\circ + m\angle C = 180^\circ \)
\( m\angle C = 180^\circ - 67^\circ = 113^\circ \)

Step1: Use supplementary angles for \( \angle B \) and \( \angle C \)

\( m\angle B + m\angle C = 180^\circ \). Given \( m\angle C = 107^\circ \):
\( m\angle B = 180^\circ - 107^\circ = 73^\circ \)

Step2: Use complementary angles for \( \angle A \) and \( \angle B \)

\( m\angle A + m\angle B = 90^\circ \). Substitute \( m\angle B = 73^\circ \):
\( m\angle A = 90^\circ - 73^\circ = 17^\circ \)

Answer:

\( m\angle B = 38^\circ \), \( m\angle C = 142^\circ \)

Problem 2