Question

Question 12(Multiple Choice Worth 2 points)

(Interior and Exterior Angles MC)
For triangle XYZ, mLX = (2g + 16)
O Interior angle = 122°; exterior angle = 58°
and the ex angle to LX measures (4g + 38)". Find the measure of LX and its exterior angle
O Interior angle = 58°; exterior angle = 122°
O Interior angle = 82°; exterior angle = 38⁰
O Interior angle = 38°; exterior angle = 82"

Answer 1

interior angle = 58°; exterior angle = 122°

Explanation:

For all polygons, an interior angle and its accompanying exterior angle are always supplementary and thus equal 180°.

Thus, we can first find g by making the sum of the equation given for the interior angle and the equation given for the exterior angle equal to 180 and solve for g:

`(2g+16)+(4g+38)=180\\2g+16+4g+38=180\\6g+54=180\\6g=126\\g=21`

Now, we can first find the measure of interior angle X by plugging in g for 21:

`X=2(21)+16\\X=42+16\\X=58`

Finally, we can find the measure of the exterior angle by either plugging in g for the equation or simply by subtracting 58 from 180 since the interior and exterior angle are supplementary and equal 180:

Exterior angle = 180 - 58

Exterior angle = 122