Question

Find the measure of the angles of an isosceles triangle where the ratio of the vertex angle to one of the base angles is 4:3

Answer 1

In this case, we'll have to carry out several steps to find the solution.

Step 01:

data:

isosceles triangle:

ratio:

4 : 3

Step 02:

geometry:

triangles:

ratio (vertex angle: base angle):

4 : 3

vertex angle = 4x

base angle = 3x

the base angles of an isosceles triangle are equal:

(4x)° + (3x)° + (3x)° = 180°

4x + 3x + 3x = 180

10x = 180

x = 180 / 10

x = 18

vertex angle = 4x = 4(18) = 72°

base angles = 3x = 3(18) = 54°

The answer is:

vertex angle = 72°

base angles = 54°