Question

hw 1.3.4 angles formed by intersecting lines
m < efd =
given ∠cfd is a right angle, find each angle.

1. m∠afb = 3x + 10, m∠bfc = 5x. find m∠efd.

Explanation:

Step1: Use angle - addition property

Since $\angle AFB$ and $\angle BFC$ are adjacent angles and $\angle AFC$ is a straight - angle ($m\angle AFC = 180^{\circ}$), we have $m\angle AFB+m\angle BFC = 180^{\circ}$. Substituting the given expressions, we get $(3x + 10)+5x=180$.

Step2: Solve the equation for x

Combining like terms, we have $8x+10 = 180$. Subtract 10 from both sides: $8x=180 - 10=170$. Then divide both sides by 8: $x=\frac{170}{8}=\frac{85}{4}=21.25$.

Step3: Find $m\angle BFC$

Substitute $x = 21.25$ into the expression for $m\angle BFC$. So $m\angle BFC=5x=5\times21.25 = 106.25^{\circ}$.

Step4: Use vertical - angle property

Since $\angle EFD$ and $\angle BFC$ are vertical angles, they are congruent. So $m\angle EFD=m\angle BFC$.

Answer:

$106.25$