To solve for the value of x, let's first understand what complementary angles are. Complementary angles are two angles whose measures add up to 90 degrees.
We know that the measure of angle P is 62 degrees and we are told that the measure of angle Q is given by the expression 3x - 14 degrees. We need to find the value of x that makes the measures of angle P and angle Q add up to 90 degrees.
We can write the equation:
Angle P + Angle Q = 90 degrees
Substituting the given measures into the equation, we get:
62 + (3x - 14) = 90
Now let's solve the equation step by step.
First, we simplify the left side of the equation by combining like terms:
3x + 62 - 14 = 90
3x + 48 = 90
Next, we isolate x by subtracting 48 from both sides of the equation:
3x + 48 - 48 = 90 - 48
3x = 42
Finally, we solve for x by dividing both sides of the equation by 3:
3x / 3 = 42 / 3
x = 14
So, the value of x is 14.
