Question

The measures of the angles of triangle ABC are given by the expressions in the table

What are the measures of angles A and C
m/A = ? Degrees
m/C = ? Degrees

Answer 1

`m<A=125\°`

`m<B=35\°`

Explanation:

step 1

Find the value of x

we know that

The sum of the interior angles in a triangle must be equal to 180 degrees

so

`m<A+m<B+m<C=180\°`

substitute the values and solve for x

`(6x-1)\°+20\°+(x+14)\°=180\°`

`7x=180\°-33\°`

`7x=147\°`

`x=147\°/7=21\°`

step 2

Find the measure of angle A

`m<A=(6x-1)\°=6(21)-1=125\°`

step 3

Find the measure of angle C

`m<C=(x+14)\°=21+14=35\°`