Lines, angles, and polygons — ACT practice questions

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Practice 59 Lines, angles, and polygons questions in the app

What this topic is

Angle facts carry most of Lines, angles, and polygons.

The interior angles of a triangle add to one hundred eighty degrees, angles on a straight line do the same, and vertical angles are equal, so many questions become a short equation in x. Polygon items extend the idea: a regular hexagon has six equal interior angles, and a regular polygon has as many lines of symmetry as it has sides.

Mixing up interior and exterior angles is the usual slip, since the exterior angles of a convex polygon always total three hundred sixty degrees. Expect ACT answer choices that include the number this slip produces.

Sample questions

Pick an answer to see whether it is right — nothing is saved, and nothing needs an account.

Question 1Easier

A certain triangle has interior angle measures of $(5 x)^{\circ}$ , $(3 x)^{\circ}$ , and $x^{\circ}$ . What is the value of $x$ ?

15✗ Not this one18✗ Not this one20✓ Correct30✗ Not this one

Show answer

Answer: C — 20

The interior angles of a triangle sum to $18 0^{\circ}$ , so $5 x + 3 x + x = 9 x = 180$ and $x = 20$ .

Question 2Mid

A square is inscribed in a circle of radius 5. What is the perimeter of the square?

10 \sqrt{2}

✗ Not this one20✗ Not this one

20 \sqrt{2}

✓ Correct40✗ Not this one

Show answer

Answer: C — $20 \sqrt{2}$

The diagonal of the square is the circle’s diameter, 10. If a side has length $s$ , then $s \sqrt{2} = 10$ , so $s = 5 \sqrt{2}$ . The perimeter is $4 s = 20 \sqrt{2}$ .

Question 3Easier

A tile is shaped like a regular pentagon. How many lines of symmetry does the tile have?

1✗ Not this one4✗ Not this one5✓ Correct10✗ Not this one

Show answer

Answer: C — 5

Each vertex of a regular pentagon determines one line of symmetry through the center and the midpoint of the opposite side, giving 5 lines.

Every question is picked for where you are right now, wrong answers come back until they stick, and it all works offline.

Practice 59 Lines, angles, and polygons questions in the app

Lines, angles, and polygons — ACT practice questions

What this topic is

Sample questions

More ACT topics

Mathematics