Question

question
△dpz can be mapped onto △wvc by a reflection. if m∠p = 39° and m∠d = 113°, find m∠c.
answer attempt 1 out of 2
m∠c be determined.

Explanation:

Step1: Use the property of reflection

Since \(\triangle DPZ\) can be mapped onto \(\triangle WVC\) by a reflection, \(\triangle DPZ\cong\triangle WVC\). So, \(\angle D\cong\angle W\), \(\angle P\cong\angle V\), \(\angle Z\cong\angle C\).

Step2: Use the angle - sum property of a triangle

The sum of the interior angles of a triangle is \(180^{\circ}\). In \(\triangle DPZ\), we know that \(m\angle D + m\angle P+m\angle Z=180^{\circ}\). Substitute \(m\angle D = 113^{\circ}\) and \(m\angle P = 39^{\circ}\) into the formula:

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Since \(\angle Z\cong\angle C\), \(m\angle C=m\angle Z\)

Answer:

\(28^{\circ}\)