a-70=b
b=2c
a+b+c=180
b+70+2c+c=180
2c+70+3c=
5c=110
c=22 deg
b=44 deg
a=114 deg
measure of angle A is 70° more than the measure of angle B. The measure of angle B is twice
the measure of angle C. Find the measure of each angle.
b=2c
a+b+c=180
b+70+2c+c=180
2c+70+3c=
5c=110
c=22 deg
b=44 deg
a=114 deg
Let's assign variables to represent the measures of angles B and C. We'll call angle B "x" and angle C "y".
Based on the information given, we can write the following equations:
1) The measure of angle A is 70° more than the measure of angle B:
A = B + 70°
2) The measure of angle B is twice the measure of angle C:
B = 2C
3) The sum of the measures of the angles of any triangle is 180 degrees:
A + B + C = 180°
Now we can substitute the second equation into the first equation to eliminate B:
A = 2C + 70°
Substituting the values of A and B into the third equation:
(2C + 70°) + (2C) + C = 180°
Simplifying the equation:
5C + 70° = 180°
5C = 110°
C = 22°
Now that we have the value of C, we can substitute it back into the second equation to find B:
B = 2C = 2 * 22° = 44°
Finally, we can substitute the values of B and C into the first equation to find A:
A = B + 70° = 44° + 70° = 114°
Therefore, the measure of angle A is 114°, the measure of angle B is 44°, and the measure of angle C is 22°.