Question

1. if m∠def = 159°, then m∠cef = ____ (9x + 4)° (5x + 15)° d e f

Explanation:

Step1: Set up an equation based on angle - addition

Since $\angle DEF=\angle DEC+\angle CEF$, and $\angle DEC=(9x + 4)^{\circ}$, $\angle CEF=(5x + 15)^{\circ}$, $\angle DEF = 159^{\circ}$, we have the equation $(9x + 4)+(5x + 15)=159$.

Step2: Combine like - terms

Combining the $x$ terms and the constant terms on the left - hand side of the equation, we get $9x+5x+4 + 15=159$, which simplifies to $14x+19 = 159$.

Step3: Solve for $x$

Subtract 19 from both sides of the equation: $14x=159 - 19$, so $14x=140$. Then divide both sides by 14: $x=\frac{140}{14}=10$.

Step4: Find the measure of $\angle CEF$

Substitute $x = 10$ into the expression for $\angle CEF$. $\angle CEF=(5x + 15)^{\circ}$, so $\angle CEF=(5\times10+15)^{\circ}=(50 + 15)^{\circ}=65^{\circ}$.

Answer:

$65^{\circ}$