Question

question 2 (4 points)
find the value of x and then find the measure of each angle.

x =

m∠nor =

m∠roq =

m∠qop =

blank 1:

blank 2:

blank 3:

blank 4:

Explanation:

Step1: Set up equation

Since $\angle NOP$ is a straight - angle and its measure is $180^{\circ}$, we have $(x + 14)+(x + 32)+(x - 10)=180$.

Step2: Simplify the left - hand side

Combine like terms: $(x+x+x)+(14 + 32-10)=180$, which gives $3x+36 = 180$.

Step3: Solve for x

Subtract 36 from both sides: $3x=180 - 36=144$. Then divide both sides by 3: $x=\frac{144}{3}=48$.

Step4: Find measure of $\angle NOR$

Substitute $x = 48$ into the expression for $\angle NOR$: $m\angle NOR=x + 14=48+14 = 62^{\circ}$.

Step5: Find measure of $\angle ROQ$

Substitute $x = 48$ into the expression for $\angle ROQ$: $m\angle ROQ=x + 32=48+32 = 80^{\circ}$.

Step6: Find measure of $\angle QOP$

Substitute $x = 48$ into the expression for $\angle QOP$: $m\angle QOP=x - 10=48-10 = 38^{\circ}$.

Answer:

Blank 1: $48$
Blank 2: $62^{\circ}$
Blank 3: $80^{\circ}$
Blank 4: $38^{\circ}$