Question

hw 1.3.2 angle bisectors and perpendicular lines
m<4 = 60
< apc is a right angle. m < bpd = m < dpe. if m < 4 = 4x+12 and m < bpe = 10x, then m < 4 = ___°

Explanation:

Step1: Note angle - relationship

Since $\angle APC$ is a right - angle, $\angle CPE$ is also a right - angle ($\angle APC+\angle CPE = 180^{\circ}$ and $\angle APC = 90^{\circ}$), so $\angle BPE=90^{\circ}$.

Step2: Set up equation

We know that $\angle BPE = 10x$ and $\angle BPE = 90^{\circ}$, so we set up the equation $10x=90$.
Solve for $x$:
$x=\frac{90}{10}=9$.

Step3: Find $\angle4$

We know that $\angle4 = 4x + 12$. Substitute $x = 9$ into the expression for $\angle4$.
$\angle4=4\times9 + 12$.
$\angle4=36+12$.
$\angle4 = 48^{\circ}$.

Answer:

$48$