Question

The measures of the base angles of an isosceles triangle are 3x 5 and 5x - 25. The measure of the vertex angle is 6x - 10. Find the measure of the vertex angle.

Answer 1

Answer: The measure of the vertex angle = 80°

Explanation:

Angle sum property of triangle : The sum of the measures of the angles for any triangle is 180 degrees.

So,

`3x+ 5 + 5x-25+6x-10= 180\\\\\Rightarrow\ 14x-30=180\\\\\Rightarrow\ 14x= 210\\\\\Rightarrow x=(210)/(14)=15`'

Then, vertex angle =
`6(15)-10=90-10= 80`

Hence, The measure of the vertex angle = 80°