Answer:
m∠Q = 43°
Step-by-step explanation:
Each of the three angles are given measurements.
Note that the total interior angle measurements of a triangle = 180°.
Set all the angles equal to 180°:
6x + 6 + 2x + 11 + 2x + 3 = 180
Simplify. Combine like terms (terms with the same amount of variables):
(6x + 2x + 2x) + (6 + 11 + 3) = 180
10x + 20 = 180
Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS. First, subtract 20 from both sides:
10x + 20 (-20) = 180 (-20)
10x = 180 - 20
10x = 160
To fully isolate x, divide 10 from both sides:
(10x)/10 = (160)/10
x = 160/10
x = 16
Your answer for x is 16. Plug in 16 for x in the given expression. Remember, you are solving for m∠Q:
m∠Q = 2x + 11
m∠Q = 2(16) + 11
m∠Q = 32 + 11
m∠Q = 43
m∠Q = 43° is your answer.
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