Question

1. which of the following is not a right triangle?

a. a triangle with angles (60^circ), (60^circ), and (60^circ)
b. a triangle with angles (20^circ), (70^circ), and (90^circ)
c. a triangle with angles (45^circ), (45^circ), and (90^circ)
d. a triangle with angles (30^circ), (60^circ), and (90^circ)

Explanation:

Step1: Recall right triangle definition

A right triangle has one 90° angle, and total angles sum to 180°.

Step2: Check option a

Sum of angles: $60^\circ + 60^\circ + 60^\circ = 180^\circ$, no 90° angle.

Step3: Verify other options

Option b: $20^\circ+70^\circ+90^\circ=180^\circ$ (has 90°).
Option c: $45^\circ+45^\circ+90^\circ=180^\circ$ (has 90°).
Option d: $30^\circ+60^\circ+90^\circ=180^\circ$ (has 90°).

Answer:

a. A triangle with angles 60°, 60°, and 60°