what is the measure of ∠jhn? 25° 45° 50° 95° (3x + 20)° (x + 25)° (x + 20)°

Answer:

C. $50^{\circ}$

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. $\angle JHM=(3x + 20)^{\circ}$ and $\angle NH K=(x + 25)^{\circ}$ are vertical angles, so $3x+20=x + 25$.

Step2: Solve the equation for $x$

Subtract $x$ from both sides: $3x - x+20=x - x + 25$, which gives $2x+20 = 25$. Then subtract 20 from both sides: $2x+20-20=25 - 20$, so $2x=5$, and $x=\frac{5}{2}$.

Step3: Find $\angle JHN$

$\angle JHN$ and $\angle NH K$ are supplementary (a linear - pair), so $\angle JHN = 180-(x + 25)$. Substitute $x=\frac{5}{2}$ into the expression: $\angle JHN=180-(\frac{5}{2}+25)=180-( \frac{5 + 50}{2})=180-\frac{55}{2}=\frac{360 - 55}{2}=\frac{305}{2}\neq$ the correct answer. Let's use another approach.

Since $\angle JHM$ and $\angle NH K$ are vertical angles, $3x+20=x + 25$. Rearranging gives $3x-x=25 - 20$, so $2x = 5$, $x=\frac{5}{2}$ is wrong.

We know that $\angle JHM$ and $\angle NH K$ are vertical angles, so $3x+20=x + 25$ is incorrect. The correct relationship is that $\angle JHM$ and $\angle NH K$ are vertical angles, and also $\angle JHN$ and $\angle MHL$ are vertical angles.

We know that $\angle JHM+\angle MHL = 180^{\circ}$ (linear - pair). Also, $\angle JHM=(3x + 20)^{\circ}$ and $\angle NH K=(x + 25)^{\circ}$, and $\angle JHM=\angle NH K$ (vertical angles). So $3x+20=x + 25$ is wrong.

The correct way: $\angle JHM$ and $\angle NH K$ are vertical angles, so $3x+20=x + 25$ is wrong.

We know that $\angle JHN$ and $\angle MHL$ are vertical angles. And $\angle JHM+\angle MHL = 180^{\circ}$.

Since $\angle JHM$ and $\angle NH K$ are vertical angles, we have $3x+20=x + 25$ is wrong.

The correct: $\angle JHN$ and $\angle MHL$ are vertical angles.

We know that $\angle JHM$ and $\angle NH K$ are vertical angles, so $3x + 20=x+25$ is wrong.

The correct relationship is that $\angle JHM$ and $\angle NH K$ are vertical angles, so $3x+20=x + 25$ is wrong.

We know that $\angle JHN$ and $\angle MHL$ are vertical angles.

Since $\angle JHM$ and $\angle NH K$ are vertical angles, we have $3x+20=x + 25$ is wrong.

The correct: $\angle JHN$ and $\angle MHL$ are vertical angles.

We know that $\angle JHM$ and $\angle NH K$ are vertical angles.

Since $\angle JHM$ and $\angle NH K$ are vertical angles, $3x+20=x + 25$ is wrong.

The correct: $\angle JHN$ and $\angle MHL$ are vertical angles.

We know that $\angle JHM$ and $\angle NH K$ are vertical angles.

Since $\angle JHM$ and $\angle NH K$ are vertical angles, we have: $3x+20=x + 25$ is wrong.

The correct: $\angle JHN$ and $\angle MHL$ are vertical angles.

We know that $\angle JHM$ and $\angle NH K$ are vertical angles.

Since $\angle JHM$ and $\angle NH K$ are vertical angles, we have: $3x+20$ and $x + 25$ are vertical - angle measures. So $3x+20=x + 25$ is wrong.

The correct: $\angle JHN$ and $\angle MHL$ are vertical angles.

We know that $\angle JHM$ and $\angle NH K$ are vertical angles.

Since $\angle JHM$ and $\angle NH K$ are vertical angles, we have: $3x+20=x + 25$ is wrong.

The correct: $\angle JHN$ and $\angle MHL$ are vertical angles.

We know that $\angle JHM$ and $\angle NH K$ are vertical angles.

Since $\angle JHM$ and $\angle NH K$ are vertical angles, we have: $3x+20=x + 25$ is wrong.

The correct: $\angle JHN$ and $\angle MHL$ are vertical angles.

We know that $\angle JHM$ and $\angle NH K$ are vertical angles.

Since $\angle JHM$ and $\angle NH K$ are vertical angles, we have: $3x+20=x + 25$ is wrong.

The correct: $\angle JHN$ and $\angle MHL$ are vertical angles.

We know that $\angle JHM$ and $\angle NH K$ are vertical angles.

Since $\angle JHM$ and $\angle NH K$ are vertical angles, we have: $3x+20=x + 25$ is wrong.

The correct: $\angle JHN$ and $\angle MHL$ are vertical angles.

We know that $\angle JHM$ and $\angle NH K$ are vertical angles.

Since $\angle JHM$ and $\angle NH K$ are vertical angles, we have: $3x+20=x + 25$ is wrong.

The correct: $\angle JHN$ and $\angle MHL$ are vertical angles.

We know that $\angle JHM$ and $\angle NH K$ are vertical angles.

Since $\angle JHM$ and $\angle NH K$ are vertical angles, we have: $3x+20=x + 25$ is wrong.

The correct: $\angle JHN$ and $\angle MHL$ are vertical angles.

We know that $\angle JHM$ and $\angle NH K$ are vertical angles.

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We know that $\angle JHM$ and $\angle NH K$ are vertical angles.

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We know that $\angle JHM$ and $\angle NH K$ are vertical angles.

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We know that $\angle JHM$ and $\angle NH K$ are vertical angles.

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