For triangle XYZ, m∠X = (5g + 18)° and the exterior angle to ∠X measures (8g + 32)°. Find the measure of ∠X and its exterior angle.
a) Interior angle = 68°; exterior angle = 112°
b) Interior angle = 112°; exterior angle = 68°
c) Interior angle = 73°; exterior angle = 105°
d) Interior angle = 105°; exterior angle = 73°
To solve this problem, we need to set up and solve an equation.
We know that the exterior angle and the interior angle are supplementary. This means that the sum of their measures is 180 degrees.
So we can set up the equation:
(5g + 18) + (8g + 32) = 180
Combining like terms, we have:
13g + 50 = 180
Subtracting 50 from both sides, we have:
13g = 130
Dividing both sides by 13, we have:
g = 10
Now we can substitute this value of g back into the expressions for the angles:
m∠X = (5g + 18)°
m∠X = (50 + 18)°
m∠X = 68°
The exterior angle is given by (8g + 32)°:
Exterior angle = (8g + 32)°
Exterior angle = (80 + 32)°
Exterior angle = 112°
Therefore, the measure of ∠X is 68° and its exterior angle measures 112°.
The correct answer is option a) Interior angle = 68°; exterior angle = 112°.