Question
3) \( m \angle E D C=167^{\circ}, m \angle E D V=29 x-1 \), and \( m \angle V D C=26 x+3 \). Find \( x \).
Ask by Wright Dawson. in the United States
Jan 30,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( x = 3 \)
Solution
Let's analyze the given information:
- \( m \angle EDC = 167^\circ \)
- \( m \angle EDV = 29x - 1 \)
- \( m \angle VDC = 26x + 3 \)
Assume that points \( E \), \( V \), and \( C \) lie on a straight line with \( D \) as the vertex. This means that the sum of the angles around point \( D \) on the straight line must equal \( 167^\circ \).
So, we have:
\[
m \angle EDV + m \angle VDC = m \angle EDC
\]
\[
(29x - 1) + (26x + 3) = 167
\]
Combine like terms:
\[
55x + 2 = 167
\]
Subtract 2 from both sides:
\[
55x = 165
\]
Divide both sides by 55:
\[
x = \frac{165}{55} = 3
\]
**Answer:** \( x = 3 \)
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Bonus Knowledge
From the given angles, we know that \( m \angle E D C + m \angle E D V + m \angle V D C = 180^\circ \) because they form a linear pair. Thus, we can set up the equation: \[ 167^\circ + (29x - 1) + (26x + 3) = 180^\circ \] Now, simplify the equation: \[ 167 + 29x - 1 + 26x + 3 = 180 \] Combine like terms: \[ (29x + 26x) + (167 - 1 + 3) = 180 \] \[ 55x + 169 = 180 \] Now, isolate \( x \): \[ 55x = 180 - 169 \] \[ 55x = 11 \] \[ x = \frac{11}{55} = \frac{1}{5} \] Therefore, \( x \) is \( \frac{1}{5} \).
