an isosceles triangle is such that the vertical angle is four times the size of a base angle.what is the size of a base angle
The sum of the angles of a triangle is 180 degrees. Yours is an isosceles triangle, and the vertical angle is four times the size of a base angle - so you've got two base angles, plus four more base angles in the vertical angle. That's six base angles in total, which means that each base angle must be 30 degrees. Check it: the vertical angle is four times a base angle, so the vertical angle is 120 degrees. 120 + 30 + 30 = 180.
20degree, 80degree, 80degree
👍 my answer
To find the size of the base angle in an isosceles triangle where the vertical angle is four times the size of a base angle, we can set up a proportional relationship.
Let's denote the measure of the base angle as x. According to the given information, the vertical angle is four times the size of the base angle.
Therefore, the measure of the vertical angle is 4x.
Since the sum of the angles in a triangle is 180 degrees, we can write the equation:
x + x + 4x = 180
Simplifying the equation:
6x = 180
Dividing both sides of the equation by 6:
x = 30
Hence, the measure of the base angle is 30 degrees.