Question

if $overrightarrow{ef}$ bisects $angle aed$, $mangle1=(4x + 3)^{circ}$ and $mangle2=(7x - 33)^{circ}$, find $mangle3.
mangle3 = select

Explanation:

Step1: Use angle - bisector property

Since $\overrightarrow{EF}$ bisects $\angle AED$, then $m\angle1 = m\angle2$. So we set up the equation $4x + 3=7x - 33$.

Step2: Solve the equation for $x$

Subtract $4x$ from both sides: $3 = 7x-4x - 33$, which simplifies to $3 = 3x - 33$. Then add 33 to both sides: $3 + 33=3x$, so $36 = 3x$. Divide both sides by 3, we get $x = 12$.

Step3: Find $m\angle1$ or $m\angle2$

Substitute $x = 12$ into the expression for $m\angle1$: $m\angle1=(4\times12 + 3)^{\circ}=(48 + 3)^{\circ}=51^{\circ}$.

Step4: Use linear - pair property

$\angle1$ and $\angle3$ form a linear - pair, so $m\angle1+m\angle3 = 180^{\circ}$. Then $m\angle3=180^{\circ}-m\angle1$. Substitute $m\angle1 = 51^{\circ}$, we get $m\angle3 = 129^{\circ}$.

Answer:

$129^{\circ}$