Triangle ABC has the following angle measures. Angle A = 44. Angle B = 4x. Angle C = 2x + 16. Find the measure of angle C.
solve for x
44 + 4x + 2x+16 = 180
sub the value of x into 2x+16
We know that the sum of the angles in a triangle is equal to 180 degrees.
So, we can write the equation as follows:
Angle A + Angle B + Angle C = 180
Substituting the given values:
44 + 4x + (2x + 16) = 180
Simplifying the equation:
44 + 4x + 2x + 16 = 180
Combining like terms:
6x + 60 = 180
Subtracting 60 from both sides:
6x = 120
Dividing both sides by 6:
x = 20
Now, we can substitute the value of x back into the equation to find the measure of angle C:
Angle C = 2x + 16
Angle C = 2(20) + 16
Angle C = 40 + 16
Angle C = 56
Therefore, the measure of angle C is 56 degrees.
To find the measure of angle C, we can use the fact that the sum of the angles in a triangle is equal to 180 degrees. Therefore, we can write the equation:
Angle A + Angle B + Angle C = 180
Substituting the given angle measures into the equation, we have:
44 + 4x + (2x + 16) = 180
Simplifying the equation, we combine like terms:
44 + 6x + 16 = 180
We can continue solving for x by first combining the constants:
60 + 6x = 180
Next, we isolate the variable by subtracting 60 from both sides:
6x = 180 - 60
6x = 120
Finally, we solve for x by dividing both sides of the equation by 6:
x = 120 / 6
x = 20
Now that we have found the value of x, we can substitute it back into the equation to find the measure of angle C:
Angle C = 2x + 16
Angle C = 2(20) + 16
Angle C = 40 + 16
Angle C = 56
Therefore, the measure of angle C is 56 degrees.