The measure of  is . Since , , and  are collinear, and the measure of  is , we know that the measure of  is .

Because the measures of the three angles in a triangle must add up to , and two of the angles in triangle  are  and , the third angle, , is .

Because line segments ZA and ZB are radii of the circle, they must have the same length. That makes triangle ABZ an isosceles triangle, with <ZAB and <ZBA having the same measure. Because the three angles of a triangle must sum to 180°, you can express this in the equation:

140 + 2x = 180 --> 2x = 40 --> x = 20

It's good to draw a diagram for this; we know that it's an isosceles triangle; remember that the angles of a triangle total 180 degrees.

Angle G for this triangle is the one angle that doesn't correspond to an equal side of the isosceles triangle (opposite side to the angle), so that means ∠F = ∠H, and that ∠F + ∠H + 40 = 180,

By substitution we find that ∠F * 2 = 140 and angle F = 70 degrees. 

An isosceles triangle has two congruent base angles and one vertex angle.  Each triangle contains .  Let  = base angle, so the equation becomes .  Solving for  gives

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

Let  = the vertex angle

and  = base angle

So the equation to solve becomes 

or

Thus the vertex angle is 38 and the base angle is 71 and their sum is 109.

This triangle has an angle of . We also know it has another angle of  at  because the two sides are equal. Adding those two angles together gives us  total. Since a triangle has total, we subtract 130 from 180 and get 50.

Because the interior angles of a triangle add up to 180°, we can create an equation using the variables given in the problem: x+2x+(3x+30)=180. This simplifies to 6X+30=180. When we subtract 30 from both sides, we get 6x=150. Then, when we divide both sides by 6, we get x=25. Because Angle B=2x degrees, we multiply 25 times 2. Thus, Angle B is equal to 50°. If you got an answer of 25, you may have forgotten to multiply by 2. If you got 105, you may have found Angle C instead of Angle B.

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

Let  = vertex angle and  = base angle.

Then the equation to solve becomes

or

.

Solving for  gives a vertex angle of 24 degrees and a base angle of 78 degrees.

Every triangle has . An isosceles triangle has one vertex ange, and two congruent base angles.

Let  be the vertex angle and  be the base angle.

The equation to solve becomes , since the base angle occurs twice.

Now we can solve for the vertex angle.

The difference between the vertex angle and the base angle is .

By rule, this is a 3-4-5 right triangle. Sine = (the opposite leg)/(the hypotenuse). This gives us 3/5.