40 points will give brainliest - what's the measure of the angle?

The 3 outside angles of a triangle need to equal 360 degrees.

You are given 96 and 137.

96 +137 = 233

The third outside angle needs to equal 360 - 233 = 127

So now you have:

2x - 23 = 127

Add 23 to both sides:

2x = 150

Divide both sides by 2:

x = 150 / 2

X = 75

The angle equals 127 degrees, X = 75