Question

if ∠aeb = 2x + 32 and ∠dec = ½x + 65, what is the value of x? a 58 b 49.5 c 22 d -22

Explanation:

Step1: Use vertical angles property

Vertical angles are equal. So, \( \angle AEB=\angle DEC \).
Given \( \angle AEB = 2x+32 \) and \( \angle DEC=\frac{1}{2}x + 65 \), we set up the equation \( 2x+32=\frac{1}{2}x + 65 \).

Step2: Solve the equation for \(x\)

Subtract \(\frac{1}{2}x\) from both sides:
\(2x-\frac{1}{2}x+32=\frac{1}{2}x-\frac{1}{2}x + 65\)
\(\frac{4x - x}{2}+32=65\)
\(\frac{3x}{2}+32 = 65\)
Subtract 32 from both sides:
\(\frac{3x}{2}+32-32=65 - 32\)
\(\frac{3x}{2}=33\)
Multiply both sides by \(\frac{2}{3}\):
\(x=33\times\frac{2}{3}\)
\(x = 22\)

Answer:

C. 22