The measure of the vertex angle in the isosceles triangle is half the measure of one base angle. What is the measure of each base angle
Wrong bot
AAAaannndd the bot gets it wrong yet again!
if the vertex angle is x, then
x + 2x + 2x = 180
x = 36
so the angles are 36,72,72
To find the measure of each base angle in an isosceles triangle when the measure of the vertex angle is known, we can follow these steps:
Step 1: Let's assign a variable to represent the measure of one base angle. Let's call it "b."
Step 2: Since the measure of the vertex angle is half the measure of one base angle, we can express it as: (1/2) * b.
Step 3: In an isosceles triangle, the sum of the angles is always 180 degrees. So, we have: b + b + (1/2) * b = 180.
Step 4: Simplify the equation by adding the like terms: 2b + (1/2) * b = 180.
Step 5: Combine the coefficients of "b": (2 + 1/2) * b = 180.
Step 6: Simplify the equation: (5/2) * b = 180.
Step 7: Divide both sides of the equation by (5/2) to isolate "b": b = (180 * 2) / 5.
Step 8: Calculate the value of "b" using a calculator: b ≈ 72.
Therefore, each base angle in the isosceles triangle measures approximately 72 degrees.