Question

Three angles of a quadrilateral are in the ratio 7 : 8 : 11 and the fourth angle is of 100°. Find the angles.

Answer 1

Given:

Three angles are in the ratio 7 : 8 : 11 and the fourth angle is 100°.

Sum of interior angles of a quadrilateral = 360°.

Step-wise calculation:

1. Let the three angles be 7x, 8x and 11x.

2. Write the sum:

7x + 8x + 11x + 100 = 360

3. Combine like terms:

26x + 100 = 360

4. Solve for x:

26x = 260

⇒ x = 10

5. Find the angles:

7x = 70°

8x = 80°

11x = 110°

And the given fourth angle = 100°.

The four angles are 70°, 80°, 110° and 100°.