In the diagram below, line RCBT and △ABC are shown with m∠A = 60 and m∠ABT = 125. What is the m∠ACR?
1.125°
2.115°
3.65°
4.55°
Answers
Answer:
3.) 65
Step-by-step explanation:
180-125=55
55+60= 115
a triangle equals 180
180-115=65
The sum of all the angles in a triangle is 180 degrees.
The value of the m∠ACR is 65°.
Option 3 is the correct answer.
What is the sum of angles in a triangle?The sum of all the angles in a triangle is 180 degrees.
We have,
Line RCBT and ΔABC.
From the diagram, we see that,
In ΔABC,
m∠A + m∠B + m∠C = 180 ___(1)
m∠CBT = 180
m∠CBA + m∠ABT = 180
m∠CBA + 125 = 180
m∠CBA = 180 - 125
m∠CBA = m∠B = 55 ____(2)
m∠BCR = 180
m∠BCA + m∠ACR = 180 ____(3)
From (1) and (2) we get,
m∠A + m∠B + m∠C = 180
60 + 155 + m∠C = 180
m∠C = 180 - 60 - 55
m∠C = 65 ____(4)
From (4) we get,
m∠ACR = 65
Thus,
The value of the m∠ACR is 65°.
Option 3 is the correct answer.
Learn more about angles here:
https://brainly.com/question/28793979
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