The image is not drawn to scale. A right triangle with a ray extending off of the vertical leg. Angle measurements of A degrees inside the triangle adjacent to an angle measurement of C degrees outside the triangle. Angle measurement of B degrees is there too.

Question

Find the value of B if C=106°
(5 points)
B=

Answer 1

Since the triangle is a right triangle, one of the angles must be 90 degrees. Let's call this angle D.

Since angle C is outside the triangle, it must be the sum of angle B and angle D, since they are adjacent angles. So we have C = B + D.

We are given that C = 106 degrees, so we can substitute that into the equation: 106 = B + D.

Since angle D is 90 degrees, we can solve for B by subtracting 90 from both sides of the equation:
106 - 90 = B.
B = 16.

Therefore, the value of B is 16 degrees.