Question

Two angles form a linear pair. The measure of one angle is (4y + 54)∘and the other angle is (2y + 90)∘. Find the measures of each angle. Do not include any units

Answer 1

The measure of each of the linear angle pair are: $78^{\circ} and 102^{\circ}$

• The linear pair angles have been illustrated in the image attached below.

• Recall:

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.

• Thus:

$(4y + 54) + (2y + 90) = 180$

• Solve for the value of y in the equation

$4y + 54 + 2y + 90 = 180$

• Add like terms

$6y + 144 = 180$

• Subtract 144 from both sides

$6y = 180 - 144\\\\6y = 36$

• Divide both sides by 6

$y = 6$

Find the measure of each angle by plugging in the value of y in each expression:

$(4y + 54) = 4(6) + 54\\\\= 24 + 54\\\\= 78^{\circ}$

$(2y + 90) = 2(6) + 90\\= 12 + 90\\\\= 102^{\circ}$

Therefore, the two angles that form the linear pair are:

$78^{\circ} and 102^{\circ}$

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