Confusing Math question!?!?

Question

I'm not that good in Math...please help me. I don't think my teachers explain it well.

Question-
Vertex angle A of isosceles triangle ABC measures 20 degrees more than 3 times angle B. Find angle C.

^ I don't understand! Please help

Answer 1

First, the definition of an isosceles triangle is that it has two equal sides. The angle between those two sides is called the "vertex" angle. The other two angles are called the "base" angles. Just like the sides being equal, the two *base angles* will be equal.

In your example you have a vertex angle A, and two base angles (B and C).

To make things simple, I'll represent the measures of the angles with variables A, B and C. We know they add up to 180 degrees, so one equation is:
A + B + C = 180°

We also know that A measures 20 degrees more than 3 times angle B.
A = 3B + 20°

Finally you know that B and C are equal:
B = C

That's 3 equations and 3 unknowns and you can solve it from there.

Start by replacing all instances of B with C (since they are equal).

Eq. 1:
A + C + C = 180°
A + 2C = 180°

Eq 2:
A = 3C + 20°

Now you have 2 equations and 2 unknowns.

Take the value for A in Eq. 2 and substitute it into Eq. 1:
(3C + 20°) + 2C = 180°
5C + 20° = 180°
5C = 160°
C = 160°/5
C = 32°

There's your answer. And just for the sake of completeness, B will also be 32° and A will be 116°.

As a double check, see that angle A (116°) is equal to 20° more than 3 times angle B (3 x 32° = 96°, 96° + 20° = 116°).

Answer 2

Draw an isosceles triangle. The vertex angle A is the one that's different. By definition, the isosceles triangle will have two base angles that are the same. The base angles are B and C.

Fact: All the angles of any triangle must add up to 180 degrees.

Let x = measure of angle B, and also angle C
Let 3x + 20 = measure of angle A

(3x + 20) +x +x = 180
5x + 20 = 180
5x = 180 -20
5x = 160
x = 32 degrees = measure of B and C
Angle A is 3(32) + 20 = 116 degrees

Check: 116 + 32 + 32 = 180?
180 = 180, check

Answer 3

Triangle ABC is isosceles. that is your biggest clue. Consider this in terms of equations:
Angle A = 20+3b.
Angle B = b
Angle C, since it is isosceles, will be the same as Angle A: 20+3b.
The total number of degrees in a triangle is 180.
So, all you have to do is equate these to 180.
(20+3b) + b +(20+3b)=180
40+7b=180
7b=140
b=20
Now, you have to plug this back into the equation for angle C.
20+(3)(20)=80. Angle C is 80, Angle A is 80, angle B is 20.