Question

∠p and ∠g form a linear pair. twice the measure of ∠g is 18° more than the measure of ∠p. what is the measure of each angle? select all that apply.
a) ( mangle p = 114^circ )
b) ( mangle p = 108^circ )
c) ( mangle p = 66^circ )
d) ( mangle g = 114^circ )
e) ( mangle g = 108^circ )
f) ( mangle g = 66^circ )
need help?

Explanation:

Step1: Define variables and linear pair property

Let \( m\angle P = x \) and \( m\angle G = y \). Since \( \angle P \) and \( \angle G \) form a linear pair, \( x + y = 180^\circ \) (linear pair angles sum to \( 180^\circ \)). Also, given that twice the measure of \( \angle G \) is \( 18^\circ \) more than the measure of \( \angle P \), so \( 2y = x + 18^\circ \).

Step2: Solve the system of equations

We have the system:

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From the first equation, \( x = 180 - y \). Substitute this into the second equation:
\( 2y=(180 - y)+ 18 \)
\( 2y = 198 - y \)
\( 2y + y = 198 \)
\( 3y = 198 \)
\( y=\frac{198}{3}=66^\circ \)

Then substitute \( y = 66^\circ \) into \( x = 180 - y \):
\( x = 180 - 66 = 114^\circ \)

So \( m\angle P = 114^\circ \) and \( m\angle G = 66^\circ \).

Answer:

A. \( m\angle P = 114^\circ \), F. \( m\angle G = 66^\circ \)