Question

which set of measures could be the angles of a triangle?
A. 35, 45, 105,
B. 62, 73, 45,
C.26, 89, 55,
D. 38, 38, 102,

Answer 1

To determine whether a set of measures can represent the angles of a triangle, the angles must satisfy two conditions:

1. Each angle must be greater than 0 degrees.
2. The sum of the angles must equal 180 degrees.

Let's check each option:

A. 35, 45, 105
Sum = 35 + 45 + 105 = 185 (not a triangle)

B. 62, 73, 45
Sum = 62 + 73 + 45 = 180 (valid triangle)

C. 26, 89, 55
Sum = 26 + 89 + 55 = 170 (not a triangle)

D. 38, 38, 102
Sum = 38 + 38 + 102 = 178 (not a triangle)

The only valid set of measures for the angles of a triangle is **B. 62, 73, 45**.