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.
Find the value of B if C=106°
(5 points)
B=
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.
To find the value of angle B, we need to use the fact that the sum of the angles in a triangle is always 180 degrees.
Given that angle C is 106 degrees, we can determine the value of angles A and B using the following relationships:
angle C + angle A + angle B = 180
Since we are given that angle C is 106 degrees, we can substitute that value into the equation:
106 + angle A + angle B = 180
Now, we need to determine the value of angle A. From the given information, we know that angle A is inside the triangle and adjacent to angle C, which is outside the triangle. Therefore, angle A and angle C are supplementary angles, meaning they add up to 180 degrees:
angle A + angle C = 180
Substituting the value of angle C, we have:
angle A + 106 = 180
Now we can solve for angle A:
angle A = 180 - 106
angle A = 74 degrees
Now we can substitute the values of angle A and C back into our original equation to find angle B:
106 + 74 + angle B = 180
Combining like terms:
180 + angle B = 180
Subtracting 180 from both sides:
angle B = 0
Therefore, the value of angle B is 0 degrees.
To find the value of angle B, we need to use the relationship between the angles in a right triangle.
In a right triangle, the sum of the angles is always equal to 180 degrees.
Let's assume angle A is the angle inside the triangle adjacent to angle C. Since angle C is given as 106 degrees, angle A would be 180 - 106 = 74 degrees.
Now, let's consider angle B. Since angle B is outside the triangle, it is a supplementary angle to angle A. In other words, the sum of angles A and B is equal to 180 degrees.
Angle A = 74 degrees
Angle A + Angle B = 180 degrees
Substituting the value of angle A into the equation:
74 + Angle B = 180
Now solve for Angle B:
Angle B = 180 - 74
Angle B = 106 degrees
Therefore, the value of angle B is 106 degrees.