Question

unit 4 triangle properties test
given△abc, where ( mangle a = 42^{circ}, mangle b = 61^{circ} ), find ( mangle c ).
( 103^{circ} )
( 180^{circ} )
( 3^{circ} )
( 77^{circ} )

Explanation:

Step1: Recall the triangle angle - sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \(m\angle A+m\angle B + m\angle C=180^{\circ}\).

Step2: Substitute the given values

We know \(m\angle A = 42^{\circ}\) and \(m\angle B=61^{\circ}\). Substitute into the formula: \(42^{\circ}+61^{\circ}+m\angle C = 180^{\circ}\).

Step3: Simplify the left - hand side

\(42 + 61=103\), so \(103^{\circ}+m\angle C=180^{\circ}\).

Step4: Solve for \(m\angle C\)

Subtract \(103^{\circ}\) from both sides: \(m\angle C=180^{\circ}- 103^{\circ}\).

Answer:

\(77^{\circ}\)