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

Answer:

D

Step-by-step explanation:

Let $\angle B=x.$ If angle A of the triangle is 1/3 as big as angle B, then $\angle A=\frac{1}{3}\angle B=\frac{1}{3}x.$. 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 $\frac{1}{3}\cdot 45^{\circ}=15^{\circ}$ and $110^{\circ}>45^{\circ}.$ True