Question

Which set of angle measures could be the interior angles of a triangle?
A
90∘,90∘,90∘90^{\circ},90^{\circ},90^{\circ}90
∘
,90
∘
,90
∘

B
80∘,80∘,200∘80^{\circ},80^{\circ},200^{\circ}80
∘
,80
∘
,200
∘

C
40∘,50∘,60∘40^{\circ},50^{\circ},60^{\circ}40
∘
,50
∘
,60
∘

D
15∘,30∘,135∘15^{\circ},30^{\circ},135^{\circ}15
∘
,30
∘
,135
∘

Answer 1

To determine which set of angle measures could be the interior angles of a triangle, we need to remember the following rules for the angles in a triangle:

1. The sum of the interior angles of a triangle must be exactly 180 degrees.
2. Each angle in a triangle must be greater than 0 degrees and less than 180 degrees.

Let's evaluate each option:

**A: \( 90^\circ, 90^\circ, 90^\circ \)**
Sum = \( 90 + 90 + 90 = 270^\circ \) (not possible)

**B: \( 80^\circ, 80^\circ, 200^\circ \)**
Sum = \( 80 + 80 + 200 = 360^\circ \) (not possible)

**C: \( 40^\circ, 50^\circ, 60^\circ \)**
Sum = \( 40 + 50 + 60 = 150^\circ \) (not possible)

**D: \( 15^\circ, 30^\circ, 135^\circ \)**
Sum = \( 15 + 30 + 135 = 180^\circ \) (possible and all angles are less than 180 degrees)

The only set of angle measures that could be the interior angles of a triangle is:

**D: \( 15^\circ, 30^\circ, 135^\circ \)**.