Answer: Since triangle QRS and triangle TUV are both triangles, we can use the fact that the sum of the interior angles in a triangle is 180 degrees.
In triangle QRS, the measure of angle Q is 117 degrees and the measure of angle R is 180 - 117 = 63 degrees. The measure of angle S is 180 - 63 = 117 degrees, since the angles in a triangle add up to 180 degrees.
In triangle TUV, the measure of angle T is 180 - 30 = 150 degrees and the measure of angle U is 30 degrees. The measure of angle V is 180 - 150 = 30 degrees, since the angles in a triangle add up to 180 degrees.
The measures of LQ and LS can be found using the fact that the exterior angle of a triangle is equal to the sum of the measures of the two interior angles that are not adjacent to it.
The measure of LQ is equal to the sum of the measures of angles R and T:
LQ = 63 + 150 = 213 degrees
The measure of LS is equal to the sum of the measures of angles Q and U:
LS = 117 + 30 = 147 degrees
So the measure of LQ is 213 degrees and the measure of LS is 147 degrees.
Explanation: