Answer:
Step-by-step explanation:
Angle GSR (27x+5) is called an "exterior" angle. It is formed by extending one side of the triangle and measuring the angle from that extension to the adjacent side of the triangle.
This exterior angle forms a linear pair with the adjacent interior angle of the triangle. That is, the sum of the exterior and interior angles at point S is 180°. If we call the interior angle "S", then ...
27x +5 = 180° - S
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You know that the sum of the three interior angles of a triangle is also 180°. That is, ...
(13x +8) + 67° + S = 180°
If we subtract S from both sides of this equation, we get ...
(13x +8) +67° = 180° - S
Substituting from above for 180 - S, we find ...
(13x +8) +67° = (27x +5)
The "shortcut" to this equation is given by the observation that ...
an exterior angle of a triangle is equal to the sum of the remote interior angles.
All we have done with this observation is condense what you already know about linear angle pairs and the triangle sum.
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27x +5 = (13x +8) +67
14x = 70 . . . . . . . . . . . . . subtract (5+13x) from both sides
x = 5 . . . . . . . . . . . divide by 14
The value of x is 5.
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Angle GSR is found using the value of x:
∠GSR = 27(5) +5 = 140°
