Question: Find the value of the varible

Explanation:

For any triangle, the interior angles always add to 180

(angle1)+(angle2)+(angle3) = 180

(w) + (4w-6) + (w) = 180

(w+4w+w) - 6 = 180

6w - 6 = 180

6w - 6+6 = 180+6 adding 6 to both sides

6w = 186

6w/6 = 186/6 divide both sides by 6

w = 31

Extra info:

This value of w leads to

4w-6 = 4*31-6 = 118

The three angles of the triangle are: 31, 118, 31

Because we have two congruent angles, this means the triangle is isosceles. The sides opposite the congruent angles are the same length.