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Answer:
x
= 50°. Why? Because both triangles have a 70° angle and a 60° angle. The last angle must be 50° in order to add up to 180°.

Here’s another one: If
, then what is ϴ?

Answer: 30°. The key here is the parallel lines. Remember the congruent angles involved with parallel lines? Sure you do. So think of them when looking at the picture: Angle
b
must be the same as angle
d
, namely 80°. Which brings us to a:

Similar Triangle Rule:
The top triangle is similar to the big triangle if their bases are parallel.

Got it? So if you see a triangle intersected by a line parallel to its base, the two triangles are similar.

Here’s some more important information on triangles.

• Pythagorean Theorem for right triangles:
a
²
+
b
²
=
c
²

• In a 30°-60°-90° triangle, the ratio of the sides is

• In a 45°-45°-90° triangle, the ratio is

Another important thing to remember about triangles is that the sum of the lengths of any two sides of a triangle must always be larger than the length of the third side.

Circles:
Here are some formulas for the components of a circle:

area = π ×
r
²
(
r
is radius)

circumference = 2 × π ×
r

arc = measure of central angle

arc also = 2 × measure of inscribed angle

Well, what the hell is all this
arc
stuff? Let us show you.

If the central angle = 30°, then the arc would also equal 30°.

As you can see, an inscribed angle is an angle made by drawing two lines from a point on a circle. The degree of the arc is always 2× that of the angle, so if the angle is 35°, the arc is 70°.

Area:
In general, area is a length times a width.

Circle:
area = π ×
r
²

Rectangle:
area =
b
×
h
(
b
is base and
h
is height, or vice versa)

Triangle:
area = ½ ×
b
×
h
(½ comes in because a triangle is ½ as large as a rectangle with the same base and height)

Volume:
In general, volume is an area times a height.

Rectangular solid:
volume = length × width × height