Question

at an archeological site, the remains of two ancient step pyramids are congruent. if abcd ≅ efgh, find m∠bad (diagrams are not to scale )

m∠bad =
(do not include the degree symbol in your answer.)

Explanation:

Step1: Use the property of congruent polygons

Since \(ABCD\cong EFGH\), corresponding angles are equal.

Step2: Identify the corresponding angle

\(\angle BAD\) corresponds to \(\angle FEH\).

Step3: Calculate \(m\angle BAD\)

The sum of angles in a quadrilateral is \(360^{\circ}\). In the second pyramid (quadrilateral \(EFGH\)), we know three angles: \(53^{\circ}\), \(127^{\circ}\), and \(127^{\circ}\). Let \(x = m\angle FEH\). Then \(x+53 + 127+127=360\).

$$x=360-(53 + 127+127)=360 - 307=53$$

Answer:

53