Question

determining angle measures
in the diagram, ( mangle3 = 120^{circ} ) and ( mangle12 = 80^{circ} ). which
angle measures are correct? check all that apply.
( square mangle1 = 60^{circ} )
( square mangle13 = 80^{circ} )
( square mangle6 = 80^{circ} )
( square mangle5 = 60^{circ} )
( square mangle10 = 120^{circ} )
( square mangle14 = 100^{circ} )

Explanation:

Step1: Use linear - pair relationship

Since \(\angle1\) and \(\angle3\) form a linear pair (\(\angle1+\angle3 = 180^{\circ}\)), and \(m\angle3=120^{\circ}\), then \(m\angle1=180 - 120=60^{\circ}\).

Step2: Use vertical - angle relationship

\(\angle12\) and \(\angle13\) are vertical angles. So \(m\angle13=m\angle12 = 80^{\circ}\) (vertical angles are equal).

Step3: Use corresponding - angle relationship

\(\angle12\) and \(\angle6\) are not corresponding angles. \(\angle5\) and \(\angle1\) are corresponding angles (because the two lines are parallel). Since \(m\angle1 = 60^{\circ}\), then \(m\angle5=60^{\circ}\) (corresponding angles of parallel lines are equal).
\(\angle10\) and \(\angle12\) are not supplementary in this non - special - angle - sum case. \(\angle14\) and \(\angle12\) are supplementary (\(\angle12+\angle14 = 180^{\circ}\)), so \(m\angle14=180 - 80=100^{\circ}\)

Answer:

\(m\angle1 = 60^{\circ}\), \(m\angle13 = 80^{\circ}\), \(m\angle5 = 60^{\circ}\), \(m\angle14 = 100^{\circ}\)