Lines, Angles, and Triangles Flashcards

An isosceles triangle has vertex angle 24° and two equal base angles. What is each base angle?

Answer: 78°

Base angles = (180° − 24°)/2 = 156°/2 = 78°.

Three lines meet at a point. The angles formed are 2x, 3x, and x. What is 3x?

Answer: 90°

If the three angles lie on a straight line: 2x + 3x + x = 180° → 6x = 180° → x = 30°; 3x = 90°.

In triangle RST, RS = 15, ST = 20, and RT = 25. Is the triangle a right triangle?

Answer: Yes, because 15² + 20² = 25²

15² + 20² = 225 + 400 = 625 = 25²; by the converse of the Pythagorean theorem, it is a right triangle.

Parallel lines are cut by a transversal. The corresponding angles are (8x − 6)° and (6x + 14)°. What is the measure of each angle?

Answer: 74°

Corresponding angles are equal: 8x − 6 = 6x + 14 → 2x = 20 → x = 10; each angle = 8(10) − 6 = 74°.

Triangle ABC has angle A = 3x, angle B = 2x + 10, and angle C = x + 20. What is angle A?

Answer: 75°

3x + 2x+10 + x+20 = 180 → 6x + 30 = 180 → x = 25; angle A = 3(25) = 75°.

Two lines are cut by a transversal. The co-interior angles are 88° and 94°. Are the lines parallel?

Answer: No, because co-interior angles must sum to 180°

88° + 94° = 182° ≠ 180°; co-interior angles of parallel lines sum to exactly 180°, so the lines are not parallel.

In triangles ABC and DEF, AB = DE = 6, BC = EF = 10, and angle B = angle E = 40°. By which congruence rule are they congruent?

Answer: SAS

Two sides and the included angle are equal (AB=DE, angle B=angle E, BC=EF), so SAS applies.