The measure of each of the linear angle pair are: [tex]78^{\circ} $ and $ 102^{\circ}[/tex]
- The linear pair angles have been illustrated in the image attached below.
Angles of a linear pair add up to give us the sum of 180 degrees. Therefore, the sum of the two angles that form the linear pair in the image attached below will equal 180 degrees.
[tex](4y + 54) + (2y + 90) = 180\\[/tex]
- Solve for the value of y in the equation
[tex]4y + 54 + 2y + 90 = 180\\\\[/tex]
[tex]6y + 144 = 180\\\\[/tex]
- Subtract 144 from both sides
[tex]6y = 180 - 144\\\\6y = 36[/tex]
[tex]y = 6[/tex]
Find the measure of each angle by plugging in the value of y in each expression:
[tex](4y + 54) = 4(6) + 54\\\\= 24 + 54\\\\= 78^{\circ}[/tex]
[tex](2y + 90) = 2(6) + 90\\= 12 + 90\\\\= 102^{\circ}[/tex]
Therefore, the two angles that form the linear pair are:
[tex]78^{\circ} $ and $ 102^{\circ}[/tex]
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