Question

If m∠GEFif thirteen less than five times m∠DEGand m∠DEF= 149°, find m∠GEF.

Answer 1

Given:

m∠DEF= 149°

m∠GEF = 5(m∠DEG) - 13

We know that:

m∠DEF = m∠GEF + m∠DEG

149 = (5(m∠DEG) - 13) + m∠DEG

149 + 13 = 5(m∠DEG) + m∠DEG

162 = 6(m∠DEG)

`m\angle\text{DEG}=\text{ }(162)/(6)\text{ = }27`

Therefore m∠DEG = 27

To find m∠GEF, we have:

m∠GEF = 5(m∠DEG) - 13

Substitute 27 for m∠DEG above:

m∠GEF = 5(27) - 13 = 135 - 13 = 122

ANSWER:

m∠GEF = 122°