Lines, Angles, and Triangles Flashcards

An exterior angle of a triangle is 155°. One remote interior angle is 85°. What is the other remote interior angle?

Answer: 70°

Exterior angle = sum of remote interior angles: 155° = 85° + x → x = 70°.

A transversal cuts two parallel lines. The angles at one intersection are all labeled. One angle is 38°. What is the value of its consecutive interior angle?

Answer: 142°

Consecutive interior (co-interior) angles sum to 180°: 180° − 38° = 142°.

Triangle ABC has AB = 5 cm, AC = 5 cm, and BC = 6 cm. What is the area of triangle ABC?

Answer: 12 cm²

Height from A to BC bisects BC (isosceles): h = √(5² − 3²) = √16 = 4; area = ½(6)(4) = 12 cm².

Lines p and q are parallel. A transversal makes a 67° angle with p. What are ALL possible angle measures formed at the intersection with q?

Answer: 67° and 113°

The transversal creates two pairs of supplementary angles: 67° and 113° appear alternately at each intersection.

In triangle LMN, side LM = 8 and side MN = 15 with a right angle at M. Which of the following is closest to angle L?

Answer: 62°

tan(L) = opposite/adjacent = MN/LM = 15/8 = 1.875; angle L ≈ arctan(1.875) ≈ 62°.

Two triangles have angle pairs: (55°, 70°, 55°) and (55°, 55°, 70°). Are they similar?

Answer: Yes, they have the same angle measures

Both triangles have angles 55°, 55°, and 70°; triangles with identical angle measures are similar (AA similarity).

Parallel lines c and d are cut by transversal e. The angle at c above the transversal on the left is (4a + 9)° and the alternate interior angle at d is (2a + 39)°. What is a?

Answer: 15

Alternate interior angles are equal: 4a + 9 = 2a + 39 → 2a = 30 → a = 15.