Answer:
Let's call the measure of the second angle x.
According to the problem, the measure of one of the angles (let's call it A) is 26 less than twice the measure of the second angle (x). So, we can write an equation:
A = 2x - 26
We also know that the measure of the third angle (let's call it B) is 35.
We know that the sum of the angles of a triangle is always 180 degrees. So we can write another equation:
A + x + B = 180
Now we can substitute the values we know into the equation and solve for x:
A = 2x - 26
A + x + B = 180
Substitute A = 2x - 26 and B = 35:
(2x - 26) + x + 35 = 180
Combine like terms:
3x + 9 = 180
Subtract 9 from both sides:
3x = 171
Divide by 3:
x = 57
So the second angle has a measure of 57 degrees.
To find the measure of the first angle (A), we can plug in x = 57 into the equation A = 2x - 26:
A = 2(57) - 26
A = 88
So the first angle has a measure of 88 degrees.
To check our work, we can add up all three angles:
88 + 57 + 35 = 180
So the measures of the three angles are 88 degrees, 57 degrees, and 35 degrees, which add up to 180 degrees as expected for a triangle.