If mZBAC = (7x + 1) º and
mZBCA = (52 + 9) . what is the
measure of the vertex angle?

Explanation:

Angle BAC can be shortened to "angle A" since the letter A is in the middle.

Angle BCA can be shortened to "angle C" for similar reasoning.

We're told that angles A and C are base angles. For any isosceles triangle, the base angles are congruent

Let's use this fact to solve for x.

angle A = angle C

7x+1 = 5x+9

7x-5x = 9-1

2x = 8

x = 8/2

x = 4

Once we know what x is, we can find each base angle

Both angles A and C are 29 degrees each, so this confirms we have the correct x value.

The last step is to use the fact that all three angles of a triangle add to 180 degrees. This will help us find angle B, which is the vertex angle.

A+B+C = 180

29+B+29 = 180

B+58 = 180

B = 180-58

B = 122

The vertex angle is 122 degrees.  

So we can say either angle B = 122, or we could say angle ABC = 122

"angle ABC" is the same as "angle CBA".

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