Question

Square ABCD and isosceles triangle BUC are drawn to create trapezoid AUCD. Square A B C D and triangle B U C are attached at side B C to create trapezoid A U C D. What is the measure of angle DCU? 45o 90o 120o 135o

Answer 1

Answer:

135°

Explanation:

The measure of angle DCU is 135°.

This is because angle DCU is the combination of a square and a triangle.

One of the angles of the square is 90° + 45° which is the value of one of the angles of an isosceles triangle.

= 135°

Answer 2

Assuming Square ABCD and isosceles triangle BUC are drawn to create trapezoid AUCD. The measure of angle DCU is 135°.

Measure of angle DCU

ΔDCB=90°

ΔCBU=90°

Hence:

ΔBCU=ΔBUC

ΔBCU=(180°-90°)/2

ΔBCU=45°

Measure of  angle DCU:

ΔDCU=ΔDCB+ΔBCU

ΔDCU=90°+45°

ΔDCU=135°

Inconclusion the measure of angle DCU is 135°.

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