Two angles of a quadrilateral measure 175° and 100°. The other two angles are in a ratio of 4:13. What are the measures of those two angles?

Answer 1

The sum of the angles in a quadrilateral is 360^o. We know that two of them measure 175^o and 100^o for a total of 275^o. This means that the two remaining angles measure 360^o - 275^o = 85^o.

The "other two angles are in a ratio of 4:13" means that we have 17 parts. 85/17 = 5

One angle is 4 x 5, so 20^o. The other is 13 x 5 = 65^o.

Check: 20/65 = 4/13

Answer 2

360-175-100=85/17=5=20°:65°.