Every triangle has 180 degrees.  An isosceles triangle has one vertex angle and two congruent base angles.

Let  = the vertex angle and  = the base angle

So the equation to solve becomes 

Thus the vertex angle is 34 and the base angles are 73.

Every triangle contains 180 degrees.  An isosceles triangle has one vertex angle and two congruent base angles.

Let  = vertex angle and  = base angle

So the equation to solve becomes .

Every triangle has 180 degrees.  An isosceles triangle has one vertex angle and two congruent base angles.

Let  = vertex angle and  = base angle

So the equation to solve becomes 

So the vertex angle is 40 and the base angles is 70

Every triangle has 180 degrees.  An isosceles triangle has one vertex angle and two congruent base angles.

Let = the vertex angle and  = the base angle

So the equation to solve becomes

The vertex angle is 32 degrees and the base angle is 74 degrees

Every triangle has 180 degrees.  An isosceles triangle has one vertex angle and two congruent base angles.

Let  = base angle and  = vertex angle

So the equation to solve becomes

Thus, 65 is the base angle and 50 is the vertex angle.

Every triangle has 180 degrees.  An isosceles triangle has one vertex angle and two congruent base angles.

Let  = base angle and  = vertex angle

So the equation to solve becomes , thus  is the base angle and  is the vertex angle.

The sum of the angles in a triangle is 180^o:  a + b + c = 180

In this case, the average of a and b is 75:

(a + b)/2 = 75, then multiply both sides by 2

(a + b) = 150, then substitute into first equation

150 + c = 180

c = 30

In a triangle, there can only be one obtuse angle. Additionally, all the angle measures must add up to 180.

The measures of the three angles are x, y, and z. Because the sum of the measures of the angles in any triangle must be 180 degrees, we know that x + y + z = 180. We can use this equation, along with the other two equations given, to form this system of equations:

x + y + z = 180

y = 2z

z = 0.5x - 30

If we can solve for both y and x in terms of z, then we can substitute these values into the first equation and create an equation with only one variable.

Because we are told already that y = 2z, we alreay have the value of y in terms of z.

We must solve the equation z = 0.5x - 30 for x in terms of z.

Add thirty to both sides.

z + 30 = 0.5x

Mutliply both sides by 2

2(z + 30) = 2z + 60 = x

x = 2z + 60

Now we have the values of x and y in terms of z. Let's substitute these values for x and y into the equation x + y + z = 180.

(2z + 60) + 2z + z = 180

5z + 60 = 180

5z = 120

z = 24

Because y = 2z, we know that y = 2(24) = 48. We also determined earlier that x = 2z + 60, so x = 2(24) + 60 = 108.

Thus, the measures of the three angles of the triangle are 24, 48, and 108. The question asks for the largest of these measures, which is 108.

The answer is 108. 

The answer is 18

We know that the sum of all the angles is 180. Using the rest of the information given we can write the other two equations:

x + y + z = 180      

x = 3y      

2x = z

We can solve for y and z in the second and third equations and then plug into the first to solve.

x + (1/3)x + 2x = 180

3[x + (1/3)x + 2x = 180]

3x + x + 6x = 540

10x = 540

x = 54

y = 18

z = 108