SOLUTION: In ΔABC, the measure of A is 17° more than four times the measure of B. The measure of C is 5° less than the measure of B. Find the measure of each angle of the triangle.

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Question 648185: In ΔABC, the measure of A is 17° more than four times the measure of B. The measure of C is 5° less than the measure of B. Find the measure of each angle of the triangle.
Answer by shweta(56) About Me  (Show Source):
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Given: In triangle ABC,
Bis measure of Angle B,A is the measure of Angle A and C of Angle C
Angle A= 17+4B ......(1)
Angle C= B-5 ......(2)
Sum of all the angles of the triangle ABCis 180 degree
Angle A+Angle B+ Angle C= 180 ....(3)
Substitute the value of A and C in equation 3
17+4B+B+B-5=180
6B+12=180
6B=180-12
6B=168
B=168/6
Angle B=28 degree
Substitute the value of B in equation 1
A=17+4B
A=17+4*28
A=17+112
Angle A=129 degree
Now substitute the value of B in equation 2 to find the value of Angle C
Angle C= B-5
Angle C= 28-5
Angle C= 23 degree
CHECK:
You can check your answer by putting in the value of all the angles in equation 3 and see if the sum is 180 degree
Angle A+Angle B+Angle C=180
129+28+23=180
Hence our answer is correct