Question

1. using square abcd, if m∠acb = (11x - 32)°, find the value of x.

Explanation:

Step1: Recall square diagonal property

In square ABCD, diagonals bisect interior angles. ∠BCD = 90°, so diagonal AC bisects it: $m\angle ACB = \frac{90^\circ}{2} = 45^\circ$.

Step2: Set up equation for x

Given $m\angle ACB = (11x - 32)^\circ$, equate to 45°:
$11x - 32 = 45$

Step3: Solve for x

Add 32 to both sides: $11x = 77$.
Divide by 11: $x = 7$.

Answer:

7