Question

A quadrilateral has two angles that measure 291° and 17°. The other two angles are in a

ratio of 4:9. What are the measures of those two angles?

Answer 1

The sum of all four angles of a quadrilateral is 360 degrees.

Let's denote the two unknown angles as 4x and 9x, where x is a constant.

We can set up an equation using the given information:

291 + 17 + 4x + 9x = 360

Simplifying the equation:

308 + 13x = 360

13x = 52

x = 4

So, the two unknown angles are:

4x = 16 degrees

9x = 36 degrees

Therefore, the measures of the two angles in a ratio of 4:9 are 16° and 36°.