Solve for x given the angles (8x + 39) and (5x + 24) of a quadrilateral.
Understand the Problem
The question asks us to solve for x given the angles of a quadrilateral. We need to use the properties of quadrilaterals to determine the relationship between the angles and set up an equation to solve for x. The angles (8x + 39) and (5x + 24) are supplementary. Supplementary angles add to 180.
Answer
$x = 9$
Answer for screen readers
$x = 9$
Steps to Solve
-
Set up the equation Since the angles are supplementary, their sum equals 180 degrees: $$ (8x + 39) + (5x + 24) = 180 $$
-
Combine like terms Combine the $x$ terms and the constant terms: $$ 13x + 63 = 180 $$
-
Isolate the x term Subtract 63 from both sides of the equation: $$ 13x = 180 - 63 $$ $$ 13x = 117 $$
-
Solve for x Divide both sides by 13: $$ x = \frac{117}{13} $$ $$ x = 9 $$
$x = 9$
More Information
In a trapezoid, the angles formed by a leg and the bases are supplementary.
Tips
A common mistake is not correctly combining like terms or making an arithmetic error when isolating $x$. Another mistake could be assuming the angles are equal instead of supplementary.
AI-generated content may contain errors. Please verify critical information
