Question

In aqrs, qs is extended through point s to point t, m/qrs = (3x 20)°, m/sqr = (x 8)°, and m/rst = (6x 18)°. find m/qrs.

a) 80°
b) 100°
c) 120°
d) 140°

Answer 1

To find the measure of angle QRS, subtract the measures of angles SQR and RST from 180 degrees. Solve for x and substitute it into the equation to find the measure of angle QRS. The answer is 140°.

Step-by-step explanation:

To find the measure of angle QRS, we can use the fact that opposite angles in a quadrilateral add up to 180 degrees. So, we have:

Measure of angle QRS = 180 - measure of angle SQR - measure of angle RST

Substituting the given angle measures, we get:

Measure of angle QRS = 180 - (3x + 20) - (6x + 18)

Now, solve for x and then substitute the value of x to find the measure of angle QRS.

Using the given answer choices, we can determine that the correct answer is (d) 140°.