In triangle ABC, m∠B = (11x − 28)° and the measure of the exterior angle to ∠B is (5x − 32)°. Find m∠B.
a) 8°
b) 16°
c) 60°
d) 137°
The exterior angle to angle B is equal to the sum of angles B and C. Therefore, we can write the equation:
(5x - 32) = (11x - 28) + C
Simplifying the equation, we have:
5x - 32 = 11x - 28 + C
-6x = C - 4
Now, we know that the angles in a triangle add up to 180 degrees. Therefore, angle A + angle B + angle C = 180. Substituting the values we are given:
(11x - 28) + (5x - 32) + C = 180
Combining like terms:
16x - 60 + C = 180
To solve this equation, we need to solve for C. Rearranging the equation:
C = 240 - 16x
Now, we can substitute this value of C back into our first equation:
-6x = (240 - 16x) - 4
-6x + 16x = 240 - 4
10x = 236
x = 23.6
Now that we have the value of x, we can substitute it back into the equation for angle B:
m∠B = 11x - 28
m∠B = 11(23.6) - 28
m∠B = 259.6 - 28
m∠B = 231.6
Therefore, the measure of angle B is approximately 231.6 degrees.
Answer: None of the above
there's an answer try again
Apologies for the error in my previous response. Let's solve the problem again.
We are given that the measure of angle B is (11x - 28)° and the measure of the exterior angle to angle B is (5x - 32)°.
The exterior angle and angle B are supplementary angles (they add up to 180 degrees). So, we can set up the equation:
(11x - 28) + (5x - 32) = 180
Combining like terms:
16x - 60 = 180
Adding 60 to both sides:
16x = 240
Dividing both sides by 16:
x = 15
Now, we can find the measure of angle B by substituting the value of x:
m∠B = 11x - 28
m∠B = 11(15) - 28
m∠B = 165 - 28
m∠B = 137
Therefore, the measure of angle B is 137 degrees.
Answer: (d) 137°