In a triangle the two larger angles differ by 10 degree. The smaller angle is 50 degree less than the largest angle. Find the measure of each angle. Just searching help on how to set it up.

A , B and C = The angles of a triangle

A = The largest angle

C = The smaller angle

B = A - 10 °

C = A - 50 °

The angles of a triangle always sum to 180 °

A + B + C = 180 °

A + A - 10 ° + A - 50 ° = 180 °

3 A - 60 ° = 180 °

3 A = 180 ° + 60 °

3 A = 240 ° Divide both sides by 3

A = 240 ° / 3

A = 80 °

B = A - 10 °

B = 80 ° - 10 °

B = 70 °

C = A - 50 °

C = 80 ° - 50 °

C = 30 °

IN A TRIANGLE THE TWO LARGER ANGLES DIFFER BY 10 DEGREE. tHE SMALLER ANGLE 50 DEGREE LESS THAN THE LARGEST ANGLE. WHAT IS THE MEASURE

To solve this problem, let's denote the three angles of the triangle as A, B, and C.

Given that the two larger angles differ by 10 degrees, we can set up the following equation:
A - B = 10.

We are also told that the smaller angle is 50 degrees less than the largest angle, so we can write this equation:
C = A - 50.

Since the sum of the angles in a triangle is always 180 degrees, we know that:
A + B + C = 180.

Now we have a system of three equations:

1) A - B = 10
2) C = A - 50
3) A + B + C = 180

To solve this system, we can use the method of substitution or elimination.

Let's use substitution to solve the system:

From equation 2, we have C = A - 50. We can substitute this expression for C into equation 3:
A + B + (A - 50) = 180.

Combining like terms, we get: 2A + B - 50 = 180.

Next, let's use equation 1 to isolate B, since we want to find the measure of each angle:
B = 10 + A.

Substituting this expression for B into the previous equation:
2A + (10 + A) - 50 = 180.

Simplifying, we have: 3A - 40 = 180.

Adding 40 to both sides, we get: 3A = 220.

Finally, divide both sides by 3: A = 220/3 ≈ 73.33.

Now that we have the value of A, we can substitute it back into equation 1 to find B:
B = 10 + A = 10 + 73.33 ≈ 83.33.

And lastly, we substitute the value of A into equation 2 to find C:
C = A - 50 = 73.33 - 50 = 23.33.

Therefore, the measures of the angles in the triangle are approximately:

Angle A ≈ 73.33 degrees.
Angle B ≈ 83.33 degrees.
Angle C ≈ 23.33 degrees.