Question

1. if (mangle efh=(5x + 1)^{circ}), (mangle hfg = 62^{circ}), and (mangle efg=(18x + 11)^{circ}), find each measure.
2. if (mangle wxz=(5x + 3)^{circ}), (mangle zxy=(8x - 4)^{circ}), and (angle wxy) is a right - angle, find each measure.

© gina wilson (all things algebra®, llc), 2014 - 2017

Explanation:

Step1: Set up equation based on angle - addition

Since $\angle EFG=\angle EFH+\angle HFG$, we have the equation $(5x + 1)+62=(18x + 11)$.
\[5x+1 + 62=18x + 11\]
\[5x+63=18x + 11\]

Step2: Solve for $x$

Subtract $5x$ from both sides:
\[63=18x-5x + 11\]
\[63 = 13x+11\]
Subtract 11 from both sides:
\[63-11=13x\]
\[52 = 13x\]
Divide both sides by 13:
\[x=\frac{52}{13}=4\]

Step3: Find $m\angle EFH$

Substitute $x = 4$ into the expression for $m\angle EFH$:
\[m\angle EFH=5x + 1=5\times4+1=20 + 1=21^{\circ}\]

Step4: Find $m\angle EFG$

Substitute $x = 4$ into the expression for $m\angle EFG$:
\[m\angle EFG=18x + 11=18\times4+11=72+11=83^{\circ}\]

Step1: Set up equation based on right - angle property

Since $\angle WXY$ is a right - angle, $m\angle WXZ+m\angle ZXY = 90^{\circ}$. So, $(5x + 3)+(8x-4)=90$.
\[5x+3+8x - 4=90\]
\[13x-1=90\]

Step2: Solve for $x$

Add 1 to both sides:
\[13x=90 + 1=91\]
Divide both sides by 13:
\[x=\frac{91}{13}=7\]

Step3: Find $m\angle WXZ$

Substitute $x = 7$ into the expression for $m\angle WXZ$:
\[m\angle WXZ=5x + 3=5\times7+3=35 + 3=38^{\circ}\]

Step4: Find $m\angle ZXY$

Substitute $x = 7$ into the expression for $m\angle ZXY$:
\[m\angle ZXY=8x-4=8\times7-4=56 - 4=52^{\circ}\]

Answer:

$x = 4$
$m\angle EFH=21^{\circ}$
$m\angle EFG=83^{\circ}$

For problem 5: