Question

in the figure below, (mangle1 = 4x^{circ}) and (mangle2=(x - 15)^{circ}). find the angle measures.

Explanation:

Step1: Set up equation

Since $\angle1$ and $\angle2$ are supplementary (linear - pair of angles), $m\angle1 + m\angle2=180^{\circ}$. So, $4x+(x - 15)=180$.

Step2: Simplify the left - hand side

Combine like terms: $4x+x-15 = 180$, which gives $5x-15 = 180$.

Step3: Isolate the variable term

Add 15 to both sides of the equation: $5x-15 + 15=180 + 15$, resulting in $5x=195$.

Step4: Solve for x

Divide both sides by 5: $x=\frac{195}{5}=39$.

Step5: Find $m\angle1$

Substitute $x = 39$ into the expression for $m\angle1$: $m\angle1=4x=4\times39 = 156^{\circ}$.

Step6: Find $m\angle2$

Substitute $x = 39$ into the expression for $m\angle2$: $m\angle2=x - 15=39-15 = 24^{\circ}$.

Answer:

$m\angle1 = 156^{\circ}$
$m\angle2 = 24^{\circ}$