Mastering Angle Relationships and Triangle Properties

A straight line is divided into three angles. If the first angle is 30 degrees and the second angle is twice the first, what is the measure of the third angle?

• 60 degrees

• 90 degrees

• 45 degrees

• 120 degrees

In a triangle, one angle measures 50 degrees and the second angle measures 70 degrees. What is the measure of the third angle?

• 70 degrees

• 50 degrees

• 60 degrees

• 80 degrees

A park has a triangular flower bed. If one side of the triangle is 10 meters long and the angle opposite this side is 60 degrees, what is the length of the side opposite the 50-degree angle if the triangle is similar to another triangle with sides of 5 meters and 8 meters?

• 9.2 meters

• 7.5 meters

• 8.66 meters

• 10.5 meters

Two lines intersect, forming four angles. If one of the angles is 120 degrees, what are the measures of the other three angles?

• 180 degrees, 0 degrees, 0 degrees, 180 degrees

• 120 degrees, 120 degrees, 60 degrees, 60 degrees

• 150 degrees, 30 degrees, 30 degrees, 150 degrees

• 90 degrees, 90 degrees, 90 degrees, 90 degrees

A triangle has sides measuring 7 cm, 24 cm, and 25 cm. Is this triangle a right triangle? Explain your reasoning using the Pythagorean theorem.

• Yes, this triangle is a right triangle.

• No, this triangle is a scalene triangle.

• No, this triangle is an obtuse triangle.

• Yes, but it does not satisfy the Pythagorean theorem.

A ladder leans against a wall, forming a right triangle with the ground. If the ladder is 15 feet long and the base of the ladder is 9 feet from the wall, how high up the wall does the ladder reach?

• 10 feet

• 14 feet

• 8 feet

• 12 feet

In a triangle, the angles are in the ratio 2:3:4. What are the measures of the angles?

• 45 degrees, 45 degrees, 90 degrees

• 40 degrees, 60 degrees, 80 degrees

• 30 degrees, 50 degrees, 100 degrees

• 20 degrees, 70 degrees, 90 degrees

A triangle has an angle that measures 90 degrees. If one of the other angles measures 30 degrees, what is the length of the side opposite the 30-degree angle if the hypotenuse is 10 cm?

• 7 cm

• 5 cm

• 3 cm

• 8 cm

Two parallel lines are cut by a transversal. If one of the alternate interior angles measures 75 degrees, what is the measure of the corresponding angle?

• 90 degrees

• 45 degrees

• 75 degrees

• 60 degrees

A triangular sign has angles measuring 40 degrees and 60 degrees. If the sign is placed on a pole, what angle does the pole make with the ground if the sign is perpendicular to the ground?

• 10 degrees

• 50 degrees

• 30 degrees

• 20 degrees