Answer:
m < T = 54°
Step-by-step explanation:
Given the following angles, whose sum add up to 180°:
m < R = 55°
m < T = (6x - 6)°
m < G = (7x + 1)°
We can establish the following formula to solve for the measure of < T:
m < R + m < T + m < G = 180°
Substitute the given values to solve for x:
55° + 6x° - 6° + 7x° + 1° = 180°
Combine like terms:
50° + 13x° = 180°
Subtract 50 from both sides:
50° - 50° + 13x° = 180° - 50°
13x° = 130°
Divide both sides by 13 to solve for x:
13x°/13 = 130°/13
x = 10
Now that we know that x = 10:
m < R = 55°
m < T = (6x - 6)° = [6(10) - 6]° = 54°
m < G = (7x + 1)° = [7(10) + 1]° = 71°
To verify that we have the correct value for x,
m < R + m < T + m < G = 180°
55° + 54° + 71° = 180°
180° = 180° (True statement. Therefore, the correct value of x = 10).
The correct measure of angle T is 54°.
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