A quadrilateral has two angles that measure 20° and 275°. The other two angles are in a ratio of 3:10. What are the measures of those two angles? A tough question for me.

Answer 1

Here's another solution.

360-275-20=65

ratio 3:10

3x+10x=65

13x=65

x=5

5*3=15° and 5*10=50°

15° and 50° are the other two angles

Answer 2

You have 2 unknowns, so you need 2 equations. Let's call the unknown angles X and Y.

The sum of the interior angles of a quadrilateral is 360 degrees. You have two totalling 295, leaving 65 for the other 2:

X + Y = 65

"The other two angles are in a ratio of 3:10"

This give you your second equation:

3X = 10Y, or X = 10Y/3

Use this to substitute for X in the first equation:

10Y/3 + Y = 65

13Y/3 = 65

Solve for Y, then use either equation to find X