Question

complete the problems 3 - 4. look at the triangles below. a. write the missing angle measure(s) for each triangle. then circle all of the right triangles. b. label each side of any right triangles as either hypotenuse or leg.

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°.

Step2: Find the missing angle for the first triangle

Let the missing angle be \(x\). Then \(x + 50^{\circ}+30^{\circ}=180^{\circ}\), so \(x=180^{\circ}-(50^{\circ} + 30^{\circ})=100^{\circ}\). Since none of the angles is 90°, it is not a right - triangle.

Step3: Find the missing angle for the second triangle

Let the missing angle be \(y\). Since the triangle is isosceles (two equal sides), the base - angles are equal. Let the base - angles be \(y\). Then \(y + y+80^{\circ}=180^{\circ}\), \(2y=180^{\circ}-80^{\circ}=100^{\circ}\), \(y = 50^{\circ}\). Since none of the angles is 90°, it is not a right - triangle.

Step4: Find the missing angle for the third triangle

Let the missing angle be \(z\). Then \(z+70^{\circ}+20^{\circ}=180^{\circ}\), so \(z = 90^{\circ}\), and it is a right - triangle.

Step5: Label the sides of the right - triangle

In the right - triangle (the third one), the side opposite the 90° angle is the hypotenuse, and the other two sides are the legs.

Answer:

a. First triangle: 100°; Second triangle: 50°; Third triangle: 90°. Circle the third triangle.
b. In the third triangle, the side opposite the 90° angle is the hypotenuse, and the other two sides are legs.