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
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
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°
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°