can somebody help me get both answers pls? ALSO PLEASE PLEASE DONT SEND YOUR LINKS

Answer:

x=30

m<G

3(30)-17

73

m<H

x+13

43

Step-by-step explanation:

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

~

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).

Solve for x and show work.

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