Question

three interior angles of a quadrilateral measure ( 55^{circ}, 117^{circ} ), and ( 120^{circ} ). what is the measure of the fourth interior angle?
( 68^{circ} )
( 78^{circ} )
( 88^{circ} )
( 98^{circ} )

Explanation:

Step1: Recall the sum of interior angles of a quadrilateral

The sum of interior angles of a quadrilateral is \((4 - 2)\times180^{\circ}=360^{\circ}\).

Step2: Let the fourth angle be \(x\)

We know that \(55^{\circ}+117^{\circ}+120^{\circ}+x = 360^{\circ}\).

Step3: Simplify the left - hand side

\(55 + 117+120+x=(55 + 117)+120+x=172+120+x = 292+x\).

Step4: Solve for \(x\)

\(292+x = 360\), then \(x=360 - 292\).
\(x = 68^{\circ}\)

Answer:

\(68^{\circ}\)