Question

△sca can be mapped onto △mbg by a rotation. if m∠a = 144° and m∠s = 28°, find m∠b. answer attempt 2 out of 3 m∠b can be determined. m∠b = °.

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. In \(\triangle SCA\), we know that \(m\angle A = 144^{\circ}\) and \(m\angle S=28^{\circ}\). Let \(m\angle C=x\). Then \(m\angle A + m\angle S+m\angle C = 180^{\circ}\).

Step2: Calculate \(m\angle C\)

Substitute the known values into the angle - sum formula: \(144^{\circ}+28^{\circ}+x = 180^{\circ}\). Simplify the left - hand side: \(172^{\circ}+x = 180^{\circ}\). Solve for \(x\): \(x=m\angle C=180^{\circ}-(144^{\circ} + 28^{\circ})=8^{\circ}\).

Step3: Use the property of rotation

Since \(\triangle SCA\) can be mapped onto \(\triangle MBG\) by a rotation, corresponding angles are equal. \(\angle B\) corresponds to \(\angle C\). So \(m\angle B=m\angle C\).

Answer:

\(8\)