Question

example 1 given ( mangle1 = 65^circ ), find the measure of each missing angle. give your reasoning

a. ( mangle2=)

b. ( mangle3=)

c. ( mangle4=)

d. ( mangle5=)

e. ( mangle6=)

f. ( mangle7=)

g. ( mangle8=)

Explanation:

Step1: Find \(m\angle2\)

\(\angle1\) and \(\angle2\) are supplementary. So \(m\angle2 = 180^{\circ}-m\angle1\).
\(m\angle2=180^{\circ} - 65^{\circ}=115^{\circ}\)

Step2: Find \(m\angle3\)

\(\angle2\) and \(\angle3\) are supplementary. So \(m\angle3 = 180^{\circ}-m\angle2\).
\(m\angle3 = 180^{\circ}-115^{\circ}=65^{\circ}\)

Step3: Find \(m\angle4\)

\(\angle1\) and \(\angle4\) are vertical angles. Vertical angles are equal. So \(m\angle4=m\angle1 = 65^{\circ}\)

Step4: Find \(m\angle5\)

\(\angle4\) and \(\angle5\) are alternate - interior angles. Alternate - interior angles are equal. So \(m\angle5=m\angle4 = 65^{\circ}\)

Step5: Find \(m\angle6\)

\(\angle5\) and \(\angle6\) are supplementary. So \(m\angle6 = 180^{\circ}-m\angle5\).
\(m\angle6=180^{\circ}-65^{\circ}=115^{\circ}\)

Step6: Find \(m\angle7\)

\(\angle6\) and \(\angle7\) are vertical angles. Vertical angles are equal. So \(m\angle7=m\angle6 = 115^{\circ}\)

Step7: Find \(m\angle8\)

\(\angle5\) and \(\angle8\) are vertical angles. Vertical angles are equal. So \(m\angle8=m\angle5 = 65^{\circ}\)

Answer:

a. \(m\angle2 = 115^{\circ}\)
b. \(m\angle3 = 65^{\circ}\)
c. \(m\angle4 = 65^{\circ}\)
d. \(m\angle5 = 65^{\circ}\)
e. \(m\angle6 = 115^{\circ}\)
f. \(m\angle7 = 115^{\circ}\)
g. \(m\angle8 = 65^{\circ}\)