Question

An isosceles triangle has an angle that measures 140 degrees. Which angles could be in the triangle?

Option 1: 80 degrees
Option 2: 40 degrees
Option 3: 140 degrees
Option 4: 20 degrees

Answer 1

An isosceles triangle with one angle measuring 140 degrees must have the other two angles equal to each other. The possible angles are 140 degrees, 140 degrees, and any positive angle that adds up to 180 degrees with the other two angles.

Step-by-step explanation:

An isosceles triangle has two equal angles. Since we know one of the angles measures 140 degrees, the other two angles must also be equal. This means that the triangle must have two angles measuring 140 degrees each and one angle measuring 180 - 2(140) = 180 - 280 = -100 degrees.

So, the possible angles in the triangle are 140 degrees, 140 degrees, and -100 degrees. However, angles in a triangle cannot be negative, so the correct answer is that the angles could be 140 degrees, 140 degrees, and any positive angle that adds up to 180 degrees with the other two angles (i.e., 180 - 140 - 140).