Question

square abcd and isosceles triangle buc are drawn to create trapezoid aucd.
what is the measure of angle dcu?
$45^circ$
$90^circ$
$120^circ$
$135^circ$

Explanation:

Step1: Identify square angle

In square ABCD, $\angle BCD = 90^\circ$.

Step2: Find isosceles triangle base angles

Isosceles $\triangle BUC$ has $BU=BC$ (from tick marks), so $\angle BUC = \angle BCU$. $\angle UBC = 90^\circ$ (supplementary to square's right angle), so:
$$\angle BCU = \frac{180^\circ - 90^\circ}{2} = 45^\circ$$

Step3: Calculate $\angle DCU$

Add $\angle BCD$ and $\angle BCU$:
$$\angle DCU = 90^\circ + 45^\circ = 135^\circ$$

Answer:

135°