If the ratio of a base angle and vertical angle of an isosceles triangle is 1:2 find the angles of the triangle
Let the base angle = x
Thus, the vertical angle = 2x
Now, sum of all the angle = 180
or, x + x + 2x = 180
or, 4x = 180
or, x = 45
Thus, angles of the triangle are 45 , 45 , 90
the same as the above.it's very perfect.
To find the angles of the isosceles triangle, we need to determine the value of the base angle.
Let's assume the measure of the base angle is x.
According to the given information, the ratio of the base angle to the vertical angle is 1:2. This means the vertical angle is twice the measure of the base angle.
Therefore, the measure of the vertical angle is 2x.
In an isosceles triangle, the base angles are congruent, meaning they have the same measure.
So we have two base angles, each measuring x.
The sum of the measures of the angles in a triangle is always 180 degrees.
Therefore, we can write the equation:
x + x + 2x = 180
Combining like terms, we get:
4x = 180
To solve for x, divide both sides by 4:
x = 180/4
x = 45
So the base angle measures 45 degrees, and the vertical angle measures twice that:
Base angle: 45 degrees
Vertical angle: 2 * 45 = 90 degrees
Therefore, the angles of the isosceles triangle are:
Base angles: 45 degrees, 45 degrees
Vertical angle: 90 degrees