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°
Accepted Solution
A:
Answer:DStep-by-step explanation:Let [tex]\angle B=x.[/tex] If angle A of the triangle is 1/3 as big as angle B, then [tex]\angle A=\frac{1}{3}\angle B=\frac{1}{3}x.[/tex]. If angle C was bigger than angle B, then [tex]\angle C>x.[/tex] 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. FalseC. 20°, 60°, 110°. Since 20°+60°+110°>180°, these angles cannot be triangle's angles. FalseD. 15°, 45°, 120°. If [tex]x=45^{\circ},[/tex] then [tex]\frac{1}{3}\cdot 45^{\circ}=15^{\circ}[/tex] and [tex]110^{\circ}>45^{\circ}.[/tex] True