Question

for questions 3 - 6, state the angle relationship(s) needed to find the missing angles and find the missing angles.

1. if ( m parallel n ) find the measure of angle 1.
2. given that the ( mangle3=(17x - 21)^{circ} ) and the ( mangle4=(8x + 1)^{circ} ), find the ( mangle8 ).( m parallel n )

Explanation:

Step1: Use the property of corresponding angles

Since \(m\parallel n\), \(\angle4=(11x - 4)^{\circ}\) and \(\angle8=(7x + 24)^{\circ}\) are corresponding angles. So \(11x-4=7x + 24\).

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Step2: Find the measure of \(\angle8\)

Substitute \(x = 7\) into \(\angle8=(7x + 24)^{\circ}\), we get \(\angle8=(7\times7+24)^{\circ}=(49 + 24)^{\circ}=73^{\circ}\).

Step3: Use the property of linear - pair angles

\(\angle1\) and \(\angle8\) form a linear - pair. So \(\angle1+\angle8 = 180^{\circ}\). Then \(\angle1=180^{\circ}-\angle8\).
Substitute \(\angle8 = 73^{\circ}\), we get \(\angle1=180^{\circ}-73^{\circ}=107^{\circ}\).

Answer:

\(107^{\circ}\)