Question

If an isosceles triangle has a vertex angle of 40 degrees, then each base angle is how many degrees?

A) 40 degrees
B) 70 degrees
C) 80 degrees
D) 140 degrees

Answer 1

To find the measure of each base angle in an isosceles triangle with a vertex angle of 40 degrees, subtract the vertex angle from 180 degrees to find the sum of the base angles, then divide by 2. Each base angle is 70 degrees.

Step-by-step explanation:

If an isosceles triangle has a vertex angle of 40 degrees, the remaining two angles are the base angles, which are equal because that is the property of an isosceles triangle. To find the measure of each base angle, we can use the fact that the sum of angles in any triangle adds up to 180 degrees.

So, we have:

• Vertex angle = 40 degrees
• Sum of angles in a triangle = 180 degrees
• Sum of base angles = 180 degrees - Vertex angle
• Sum of base angles = 180 degrees - 40 degrees
• Sum of base angles = 140 degrees
• Each base angle = Sum of base angles / 2
• Each base angle = 140 degrees / 2
• Each base angle = 70 degrees

Therefore, the correct answer is B) 70 degrees.