Question

find the measure of ∠ilf.
a) are the angles congruent or supplementary? congruent(∠1 = ∠2) supplementary(∠1+∠2 = 180°)
b) solve for x. check your work: keep trying. youve tried 1 times.
c) solve for the measure of ∠ilf. check your work: keep trying. youve tried 1 times.

Explanation:

Step1: Identify angle - relationship

The angles $(7x + 21)^{\circ}$ and $(8x + 69)^{\circ}$ are supplementary since they are same - side interior angles formed by two parallel lines $GH$ and $IJ$ cut by a transversal $EF$. So, $(7x + 21)+(8x + 69)=180$.

Step2: Solve the equation for x

Combine like terms:
\[

$$\begin{align*} 7x+21 + 8x+69&=180\\ 15x+90&=180\\ 15x&=180 - 90\\ 15x&=90\\ x&=\frac{90}{15}\\ x& = 6 \end{align*}$$

\]

Step3: Find the measure of $\angle ILF$

Substitute $x = 6$ into the expression for $\angle ILF=(8x + 69)^{\circ}$.
\[

$$\begin{align*} \angle ILF&=8\times6+69\\ &=48 + 69\\ &=117^{\circ} \end{align*}$$

\]

Answer:

a) Supplementary$(\angle1+\angle2 = 180^{\circ})$
b) $x = 6$
c) $117^{\circ}$