Find measures of angles using Algebra

Angle P and angle Q are complementary. the measure of angle P is two more than 10 times the measure of angle Q.  What is the measure of each angle?

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Complementary angles add up to 90°.

x = angle Q
10x + 2 = angle P   {angle P is two more than ten times angle Q}

x + 10x + 2 = 90   {the two angles add up to 90°}
11x + 2 = 90   {combined like terms}
11x = 88   {subtracted 2 from both sides}
x = 8   {divided both sides by 11}
10x + 2 = 82   {substituted 8, in for x, into 10x + 2}

angle Q = 8
angle P = 82

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