Find x Using Square Diagonal Angle Bisector Property - Math Solver AI

$Math Problem$

Mathematics Grade 8 (Junior High School)

Question Content

In square ABCD with diagonals intersecting at E, m∠ACB = (11x - 32)°. Find the value of x.

Correct Answer

x = 7

Detailed Solution Steps

1
Step 1: The diagonal of a square bisects the 90° interior angle, so ∠ACB = 45°.
2
Step 2: Set up the equation: \(11x - 32 = 45\).
3
Step 3: Solve for x: Add 32 to both sides: \(11x = 77\). Divide both sides by 11: \(x = 7\).

Knowledge Points Involved

1

Square Diagonals Bisect Interior Angles

Each diagonal of a square splits a 90° interior angle into two 45° angles, which is used to find the measure of angles formed by a side and a diagonal.

2

Solving One-Variable Linear Equations

For equations in the form \(ax - b = c\), isolate the variable by first adding the constant term to both sides, then dividing by the coefficient of x.

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