Question

Felicity drew a triangle on her paper. Angle A of the triangle was 1/3 as big as angle B. Angle C was bigger than angle B. Which list can represent the angle measures in this triangle? A. 30°, 60°, 90° B. 25°, 55°, 100° C. 20°, 60°, 110° D. 15°, 45°, 120°

Answer 1

D

Explanation:

Let
`\angle B=x.` If angle A of the triangle is 1/3 as big as angle B, then
`\angle A=(1)/(3)\angle B=(1)/(3)x.`. If angle C was bigger than angle B, then
`\angle C>x.` Consider all options:

A. 30°, 60°, 90°. Angles 30° and 90° can be anglea A and B, But 60°<90°. False.

B. 25°, 55°, 100°. Here are no angles such that one of them is three times greater. False

C. 20°, 60°, 110°. Since 20°+60°+110°>180°, these angles cannot be triangle's angles. False

D. 15°, 45°, 120°. If
`x=45^(\circ),` then
`(1)/(3)\cdot 45^(\circ)=15^(\circ)` and
`110^(\circ)>45^(\circ).` True