Question

2.

• ( mangle1=)__________
• ( mangle2=)__________
• what is the relationship between ( angle1) and ( angle3)?__________

3.

• ( angle1) and ( angle4) are__________
• ( angle4) and ( angle5) are________ and________
• which angle is complementary to ( angle2)?__________
• which angles are adjacent to ( angle3)?__________

4.

• ( angle4) and ( angle5) are complementary and the ( mangle4) is ( 46^{circ}). find the remaining measurements.

( mangle1=)_____, ( mangle2=)___, ( mangle3=)_____
( mangle5=)_____, ( mangle6=)_____

Explanation:

Step1: Find \(m\angle1\)

Since \(\angle1\) and the \(100^{\circ}\) angle are supplementary (they form a linear pair), \(m\angle1 = 180^{\circ}- 100^{\circ}=80^{\circ}\)

Step2: Find \(m\angle2\)

\(\angle2\) and the \(100^{\circ}\) angle are vertical angles. Vertical angles are equal, so \(m\angle2 = 100^{\circ}\)

Step3: Relationship between \(\angle1\) and \(\angle3\)

\(\angle1\) and \(\angle3\) are vertical angles.

Answer:

\(m\angle1 = 80^{\circ}\), \(m\angle2 = 100^{\circ}\), \(\angle1\) and \(\angle3\) are vertical angles.