Geometry

If two parallel lines are cut by a transversal, which of the following pairs of angles are always equal?

If an interior angle of a regular polygon is $120^\circ$, what is its exterior angle?

A regular polygon has an exterior angle of $20^\circ$. How many sides does it have?

In cyclic quadrilateral $XYZW$, if $\angle X = 3\angle Z$, find the size of $\angle Z$.

$PT$ is a tangent to a circle at $T$, and $O$ is the center. If $OT = 9$ and $PT = 40$, find the distance $OP$.

$A, B, C$ are points on a circle with center $O$. If $\triangle OAB$ is isosceles with $OA=OB$ and $\angle AOB = 100^\circ$, find $\angle ACB$ on the major arc.

If two right-angled triangles have the same non-right angle, they must be:

Two similar triangles $ABC$ and $PQR$ have areas $18\text{ cm}^2$ and $32\text{ cm}^2$. What is the ratio of side $AB$ to side $PQ$?

If the volume of a sphere is increased by a factor of $8$, by what factor does its surface area increase?

What is the order of rotational symmetry for a regular octagon?

How many lines of symmetry does the letter $H$ have?

How many planes of symmetry does a pyramid with an equilateral triangular base and three congruent isosceles triangles as its side faces have?