Lines, Angles, and Triangles Flashcards

An angle is 14° more than its complement. What is the angle?

Answer: 52°

x + (x − 14) = 90° → 2x = 104° → x = 52°.

Triangle XYZ has angle X = (4k + 5)°, angle Y = (2k + 15)°, angle Z = (6k − 20)°. What is angle Z?

Answer: 70°

4k+5+2k+15+6k−20=180 → 12k=180 → k=15; angle Z = 6(15)−20 = 70°.

An isosceles triangle has perimeter 50 cm and base 14 cm. What are the two equal sides?

Answer: 18 cm

2s + 14 = 50 → s = 18 cm.

In similar triangles, the ratio of similarity is 3:4. The smaller triangle has altitude 12. What is the larger triangle's altitude?

Answer: 16

3/4 = 12/h → h = 48/3 = 16.

An exterior angle of a triangle is (5x + 3)°. The two remote interior angles are (2x + 5)° and (x + 6)°. What is x?

Answer: 4

5x+3 = (2x+5)+(x+6) → 5x+3 = 3x+11 → 2x=8 → x=4. Check: 5(4)+3=23; (2(4)+5)+(4+6)=13+10=23. ✓

Two parallel lines are cut by a transversal. Co-interior angles are (4n + 10)° and (2n + 26)°. What is n?

Answer: 24

(4n+10)+(2n+26)=180 → 6n+36=180 → 6n=144 → n=24.

Triangle ABC ≅ Triangle DEF (by SAS): AB = DE = 8, angle B = angle E = 50°, BC = EF = 6. What can be concluded?

Answer: AC = DF

By SAS congruence, all corresponding parts are equal; AC corresponds to DF, so AC = DF.