Question

what is the measure of \\( \angle jhn \\)?
\\( 25 ^ { \circ } \\)
\\( 45 ^ { \circ } \\)
\\( 50 ^ { \circ } \\)
\\( 95 ^ { \circ } \\)

Explanation:

Step1: Use the property of a straight line (sum of angles on a straight line is \(180^{\circ}\))

$$(3x + 20)+(x + 25)+(x + 20)=180$$

Step2: Combine like - terms

$$3x+x+x+20 + 25+20=180$$
$$5x+65 = 180$$

Step3: Solve for \(x\)

Subtract \(65\) from both sides:
$$5x=180 - 65$$
$$5x=115$$
Divide both sides by \(5\):
$$x=\frac{115}{5}=23$$

Step4: Find the measure of \(\angle JHN\)

Substitute \(x = 23\) into \((x + 27)\) (since \(\angle JHN=(x + 27)\) as per the vertical - angle relationship and angle - sum property).
$$\angle JHN=x + 27=23+27 = 50^{\circ}$$

Answer:

C. \(50^{\circ}\)