Question

1. ∠1 and ∠2 form a linear pair. the measure of ∠2 is six more than twice the measure of ∠1. find m∠2.

Explanation:

Step1: Define variables and linear pair property

Let \( m\angle 1 = x \). Since \( \angle 1 \) and \( \angle 2 \) form a linear pair, they are supplementary, so \( m\angle 1 + m\angle 2 = 180^\circ \). Also, \( m\angle 2 = 2x + 6 \) (six more than twice \( \angle 1 \)).

Step2: Set up and solve the equation

Substitute \( m\angle 2 \) into the supplementary angle equation: \( x + (2x + 6) = 180 \). Combine like terms: \( 3x + 6 = 180 \). Subtract 6 from both sides: \( 3x = 174 \). Divide by 3: \( x = 58 \).

Step3: Find \( m\angle 2 \)

Substitute \( x = 58 \) into \( m\angle 2 = 2x + 6 \): \( m\angle 2 = 2(58) + 6 = 116 + 6 = 122 \).

Answer:

\( 122^\circ \)