square abcd and isosceles triangle buc are drawn to create trapezoid aucd. what is the measure of angle dcu…

Explanation:

Step1: Recall properties of square

In square (ABCD), each angle is (90^{\circ}), so (\angle BCD = 90^{\circ}).

Step2: Recall properties of isosceles - right - triangle

Since (\triangle BUC) is an isosceles right - triangle, (\angle BCU=45^{\circ}).

Step3: Calculate (\angle DCU)

(\angle DCU=\angle BCD+\angle BCU). Substitute (\angle BCD = 90^{\circ}) and (\angle BCU = 45^{\circ}) into the formula. So (\angle DCU=90^{\circ}+45^{\circ}=135^{\circ}).

Answer:

(135^{\circ})