Question

1. if m∠gef is ten less than four times m∠deg and m∠def = 145, find m∠deg and m∠gef

Explanation:

Step1: Set up equations

Let $x = m\angle DEG$. Then $m\angle GEF=4x - 10$. Since $\angle DEF=\angle DEG+\angle GEF$ and $m\angle DEF = 145$, we have the equation $x+(4x - 10)=145$.

Step2: Simplify the equation

Combine like - terms: $x + 4x-10=145$ becomes $5x-10 = 145$.

Step3: Solve for $x$

Add 10 to both sides of the equation: $5x-10 + 10=145 + 10$, so $5x=155$. Then divide both sides by 5: $x=\frac{155}{5}=31$.

Step4: Find $m\angle GEF$

Substitute $x = 31$ into the expression for $m\angle GEF$. $m\angle GEF=4x - 10=4\times31-10=124 - 10 = 114$.

Answer:

$m\angle DEG = 31$, $m\angle GEF=114$