two angles of a quadrilateral measure 94* and 244*. the other two angles are in a ratio of 4:17. what are the measures of those two angles?

Question

two angles of a quadrilateral measure 94* and 244*. the other two angles are in a ratio of 4:17. what are the measures of those two angles?

Answer 1

The sum of the measures of the 4 angles of a quadrilateral is 360°.

If two numbers are in the ratio 4:17, those numbers could be 4 and 17, or 8 and 34, or even 2 and 17/2. That means there is some constant that can be multiplied times the 4 and 17 to get the original numbers. Let k be that multiplier.

The unknown angles can then be represented as 4k and 17k.

We can write the equation 94 + 244 + 4k + 17k = 360.

338 + 21k = 360

21k = 22

k = 22/21

So one of the angles is 4(22/21) = 88/21.

The 2nd is 17(22/21) = 374/21.

Visit this graph to see that the sum of the four angles is 360.

desmos.com/calculator/tjhgzyf7yx