Question

If m∠GEF is nine less than five times twice of m∠DEG and m∠DEF = 152°, find m∠GEF

Answer 1

m∠GEF is approximately 124.15°.

Explanation:

Given that m∠DEF = 152°, we can use the following equation to find m∠GEF:

m∠GEF = 5m∠DEG - 9

We need to find m∠GEF. To do that, we need to find m∠DEG first. We can use the following equation to find m∠DEG:

m∠DEF = m∠DEG + m∠GEF

Substituting the value of m∠GEF from the first equation into the second equation, we get:

152 = m∠DEG + (5m∠DEG - 9)

Simplifying the equation, we get:

152 = 6m∠DEG - 9

Adding 9 to both sides of the equation, we get:

161 = 6m∠DEG

Dividing both sides of the equation by 6, we get:

m∠DEG = 26.83°

Now that we know m∠DEG, we can substitute it into the first equation to find m∠GEF:

m∠GEF = 5(26.83) - 9

m∠GEF = 124.15°

Therefore, m∠GEF is approximately 124.15°.