Question

question
△szo ≅ △avl. if m∠o = 16° and m∠z = 144°, find m∠a.
answer attempt 1 out of 2
m∠a be determined.

Explanation:

Step1: Use the triangle angle - sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). For \(\triangle SZO\), we know that \(m\angle S+m\angle Z + m\angle O=180^{\circ}\).

Step2: Substitute the given angle measures

Substitute \(m\angle O = 16^{\circ}\) and \(m\angle Z = 144^{\circ}\) into the equation: \(m\angle S+144^{\circ}+16^{\circ}=180^{\circ}\). Then \(m\angle S=180^{\circ}-(144^{\circ} + 16^{\circ})=180^{\circ}-160^{\circ} = 20^{\circ}\).

Step3: Use the property of congruent triangles

Since \(\triangle SZO\cong\triangle AVL\), corresponding angles are equal. That is, \(\angle S\) and \(\angle A\) are corresponding angles. So \(m\angle A=m\angle S\).

Answer:

\(20^{\circ}\)