The sum of the measures of the angles of any triangle is 180 degrees. In triangle abc, angles a and b have the same measure, while the measure of angle c is 78 degrees larger than each of a and b. What are the measures of the three angles?
angle a is __degrees.
a+b+c = 180
b = a
c = a+78
so,
a + a + a+78 = 180
3a = 102
a = 34
so, b=34 and c=112
The sum of the angles of a triangle is 180 degrees. In the figure below angle B and angle C are the same size. If angle A is 54 degrees smaller than angle B. Find the measure of each angle.
angle a is definitely some degrees
To find the measure of angle a in triangle ABC, we need to set up an equation and solve for it.
We know that angles a and b have the same measure, so let's represent their measurement as 'x'.
According to the problem, the measure of angle c is 78 degrees larger than each of angles a and b. Therefore, the measure of angle c can be represented as 'x + 78'.
Using the fact that the sum of the measures of the angles of any triangle is 180 degrees, we can write the equation:
x + x + (x + 78) = 180
Now, let's solve for x:
2x + x + 78 = 180
Combining like terms, we have:
3x + 78 = 180
Subtracting 78 from both sides of the equation:
3x = 180 - 78
3x = 102
Dividing both sides by 3:
x = 102 / 3
x = 34
Therefore, angle a measures 34 degrees.