Two angles of a quadrilateral measure 140° and 50°. The other two angles are in a ratio of 7:10. What are the measures of those two angles?

2 answers

Let the other two angles be 7x and 10x
The angles of a quad add up to 360°
so 140+50+7x+10x = 360

solve for x, then evaluate 7x and 10x
The interior angles of a quadrilateral measure to 360°

Two of them are known and are 140° and 50°

Sum of these two angles is:

140° + 50° = 190°

The other two angles must sum to:

360° - 190° = 170°

Mark the other two angles as A and B

A + B = 170°

The other two angles are in a ratio of 7:10 means:

A / B = 7 / 10

Cross multiply

10 A = 7 B

Divide both sides by 10

A = 7 / 10 B

Replace A with 7 / 10 B in formula

A + B = 170°

7 / 10 B + B = 170°

7 / 10 B + 10 B / 10 = 170°

17 B / 10 = 170°

Multiply both sides by 10

17 B = 1700°

Divide both sudes by 17

B = 100°

A = 7 / 10 B

A = 7 • 100° / 10

A = 700° / 10

A = 70°

The measures of other two angles are:

70° and 100°