Answer:
m∠G = 73°
m∠H = 43°
Step-by-step explanation:
Use the exterior angle theorem. The exterior angle theorem states that the exterior angle's measurement will be the sum of the two opposite interior angles. Set the equation:
(3x - 17) + (x + 13) = 116
First, combine like terms by simplifying:
3x + x - 17 + 13 = 116
4x - 4 = 116
Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS. PEMDAS is the order of operation, and stands for:
Parenthesis
Exponents (& Roots)
Multiplication
Division
Addition
Subtraction
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First, add 4 to both sides of the equation:
4x - 4 = 116
4x - 4 (+4) = 116 (+4)
4x = 116 + 4
4x = 120
Next, divide 4 from both sides of the equation:
(4x)/4 = (120)/4
x = 120/4
x = 30
Plug in 30 for x for each angle measurement:
m∠G = 3x - 17
m∠G = 3(30) -17
m∠G = 90 - 17
m∠G = 73°
m∠H = x + 13
m∠H = 30 + 13
m∠H = 43°
Check:
180 - 73 - 43 = 64 (Summation of a triangle's angle).
180 - 64 = 116 (Theorem of line).
