Answer:
Exterior angle: 86°
Base angle: 43°
Base angle: 43°
Third angle: 94°
Explanation:
First we'll find x, then calculate all the angles.
There is a mark on two of the sides of the triangle. Two sides are the same. This is an isosceles triangle. So that means the base angles are the same also. One is marked 5x - 12, so the other base angle is also 5x - 12.
The marked exterior angle has a special relationship with the two remote interior angles.
If you add the two remote interior angles it equals the exterior angle.
8x-2 = 5x-12 + 5x-12
Combine like terms.
8x - 2 = 10x - 24
Subtract 8x.
-2 = 2x - 24
Add 24.
22 = 2x
Divide by 2.
11 = x
Now we can find all the angles.
The exterior angle is 8x - 2
= 8(11) - 2
= 88 - 2
= 86°
Base angle is 5x - 12
= 5(11) - 12
= 55 - 12
= 43°
The last angle in the triangle is a linear pair with the exterior angle. Or (Also,) the three angles in the triangle add up to 180°.
Angle+43°+43°=180°
Angle + 86 = 180
Angle = 94°