Mastering Angles and Triangle Properties Challenge

A triangle has two angles measuring 45 degrees and 65 degrees. What is the measure of the third angle?

• 70 degrees

• 80 degrees

• 60 degrees

• 90 degrees

In a right triangle, one angle measures 30 degrees. What is the measure of the other non-right angle?

• 90 degrees

• 75 degrees

• 60 degrees

• 45 degrees

A triangle has sides of lengths 7 cm, 24 cm, and 25 cm. Is this triangle a right triangle? Explain your reasoning.

• Yes, this triangle is a right triangle.

• No, the sides do not form a triangle at all.

• Yes, but only if the longest side is opposite the right angle.

• No, this triangle is not a right triangle because it does not satisfy the Pythagorean theorem.

A ladder leans against a wall forming a right triangle with the ground. If the ladder is 10 feet long and the base is 6 feet from the wall, what angle does the ladder make with the ground?

• 90 degrees

• 75 degrees

• 53.13 degrees

• 30 degrees

In triangle ABC, angle A measures 50 degrees and angle B measures 70 degrees. What is the measure of angle C?

• 90 degrees

• 60 degrees

• 50 degrees

• 70 degrees

A triangular park has one angle measuring 90 degrees and the other two angles measuring 40 degrees and 50 degrees. What type of triangle is this?

• Right triangle

• Scalene triangle

• Isosceles triangle

• Equilateral triangle

A triangle has sides of lengths 5 cm, 12 cm, and 13 cm. Determine if this triangle is acute, right, or obtuse.

• isosceles

• right

• scalene

• acute

In triangle DEF, angle D is twice the measure of angle E, and angle F is 30 degrees. Find the measures of angles D and E.

• Angle D: 90 degrees, Angle E: 45 degrees

• Angle D: 80 degrees, Angle E: 40 degrees

• Angle D: 100 degrees, Angle E: 50 degrees

• Angle D: 120 degrees, Angle E: 60 degrees

A triangular sail has one angle measuring 60 degrees and the other two angles are equal. What are the measures of the other two angles?

• 90 degrees each

• 30 degrees each

• 60 degrees each

• 45 degrees each

A construction worker needs to find the height of a triangular roof. If the base of the roof is 12 feet and the angles at the base are both 45 degrees, what is the height of the roof?

• 10 feet

• 4 feet

• 8 feet

• 6 feet