Question

which two equations relate the measure of ∠4, to the measures of ∠1, ∠2, and/or ∠3. a. m∠4 = m∠1 + m∠2 b. m∠4 = m∠2 + m∠3 c. m∠4 = 180° - m∠3 d. m∠4 = 180° - (m∠3 + m∠2)

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. So, \(m\angle1 + m\angle2+m\angle3 = 180^{\circ}\).

Step2: Recall linear - pair property

\(\angle3\) and \(\angle4\) form a linear - pair. So, \(m\angle3 + m\angle4=180^{\circ}\), which implies \(m\angle4 = 180^{\circ}-m\angle3\).

Step3: Substitute and simplify

From \(m\angle1 + m\angle2+m\angle3 = 180^{\circ}\), we can get \(m\angle1 + m\angle2=180^{\circ}-m\angle3\). Since \(m\angle4 = 180^{\circ}-m\angle3\), then \(m\angle4=m\angle1 + m\angle2\).

Answer:

A. \(m\angle4 = m\angle1 + m\angle2\)
C. \(m\angle4 = 180^{\circ}-m\angle3\)