Calculate the remaining angles in the isosceles triangle below.
We have hundreds of course questions with personalized recommendations + Account 100% premium
Calculate the remaining angles in the isosceles triangle below.
Since we know that the triangle is isosceles, we know that the base angles are equal.
That is:
Now we can calculate the vertex angle.
Since the sum of angles in a triangle is equal to 180 degrees, we will calculate the vertex angle as follows:
Therefore, the values of the angles are 80, 50, and 50.
Find the measure of the angle \( \alpha \)
The base angles are the two angles opposite the equal sides. In this triangle, angles B and C are at the bottom (the base), so they're equal. The vertex angle A is at the top where the two equal sides meet.
If you know the vertex angle, subtract it from 180°, then divide by 2 to find each base angle. For example: vertex = 80°, so each base angle = (180° - 80°) ÷ 2 = 50°.
Yes! If the vertex angle is 90°, then each base angle would be 45°. This creates a right isosceles triangle, which is very common in geometry problems.
In an isosceles triangle, the two sides of equal length create identical conditions at their endpoints. This symmetry forces the angles opposite these equal sides to be equal too.
Get unlimited access to all 18 Angles questions, detailed video solutions, and personalized progress tracking.
Unlimited Video Solutions
Step-by-step explanations for every problem
Progress Analytics
Track your mastery across all topics
Ad-Free Learning
Focus on math without distractions
No credit card required • Cancel anytime