Question

angles of triangles quick check
if a triangle has a 22° angle and a 46° angle, what can be established about the third angle measure and the type of triangle? (1 point)
the third angle measure is 68°, and the triangle is an obtuse triangle.
the third angle measure is 128°, and the triangle is an obtuse triangle.
the third angle measure is 112°, and the triangle is an acute triangle.
the third angle measure is 112°, and the triangle is an obtuse triangle.

Explanation:

Step1: Use the triangle angle sum formula

The sum of angles in a triangle is \(180^{\circ}\). Let the third angle be \(x\). Then \(x + 22^{\circ}+46^{\circ}=180^{\circ}\).

Step2: Solve for \(x\)

\(x=180^{\circ}-(22^{\circ} + 46^{\circ})=180^{\circ}-68^{\circ}=112^{\circ}\).

Step3: Classify the triangle

Since \(112^{\circ}>90^{\circ}\), the triangle is obtuse.

Answer:

The third angle measure is \(112^{\circ}\), and the triangle is an obtuse triangle.