Algebraic Side-Angle Properties
publish date: 2026/05/16 01:15:6.405235 UTC
In trapezoid ABCD, the top horizontal base side AB is parallel to the bottom horizontal base side DC (\(AB \parallel DC\)). The measures of the interior angles adjacent to leg AD are algebraically expressed as:
• \(m\angle A = (3x + 15)^\circ\)
• \(m\angle D = (2x - 10)^\circ\)
Solve the linear equation to discover the correct value of the variable \(x\).
Correct Answer
Explanation
Because line segment AB is parallel to line segment DC, the angles positioned on the same side of leg line AD comprise a pair of consecutive interior angles. This means they are supplementary and their sum equals \(180^\circ\).
Set up the algebraic addition:
\[ m\angle A + m\angle D = 180^\circ \]
\[ (3x + 15) + (2x - 10) = 180 \]
Combine like terms:
\[ 5x + 5 = 180 \]
Isolate the variable term:
\[ 5x = 175 \]
\[ x = 35 \]
Reference
Mathematics for college students, go-math-science.com