in a triangle, the measure of the first angle is four times the measure of thesecond angle.The measure of the third angle 78 more than the second angle. What is the measure of the first angle?
Let x = first angle, the 4x = second angle and 4x + 78 = third angle. For a triangle, they should add up to 180º. Solve for x.
To find the measure of the first angle, let's assign variables to each angle.
Let's say the measure of the second angle is x degrees.
According to the problem, the measure of the first angle is four times the measure of the second angle, so the first angle would be 4x degrees.
The measure of the third angle is given as 78 more than the second angle, so the third angle would be x + 78 degrees.
In a triangle, the sum of all three angles is always 180 degrees.
Therefore, we can add the measures of the three angles and set it equal to 180:
4x + x + (x + 78) = 180
Now, we can solve the equation to find the value of x, which will give us the measure of the first angle:
Combine like terms:
6x + 78 = 180
Subtract 78 from both sides of the equation:
6x = 180 - 78
6x = 102
Divide both sides of the equation by 6:
x = 102/6
x = 17
Now that we know the value of x, we can substitute it into the expression for the first angle:
First angle = 4x
First angle = 4 * 17
First angle = 68
Therefore, the measure of the first angle is 68 degrees.