Lines, angles, and polygons — ACT practice questions

On the ACT Mathematics test, Lines, angles, and polygons covers intersecting lines, interior and exterior angles, and the sides and symmetries of triangles, quadrilaterals, and regular polygons. A student must solve for unknown angle measures, find a perimeter when a polygon is inscribed in a circle, and count lines of symmetry of a regular figure. Questions are multiple choice and typically offer five numeric answers. Common traps include using the wrong angle sum, treating a radius as a side of an inscribed square, and mixing reflection symmetry with rotational symmetry.

Section: Mathematics 45 questions on the paper
57 practice questions in the app

Sample questions

Question 1

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

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Answer: C — 20

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

Question 2

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

A $10\sqrt{2}$
B20
C $20\sqrt{2}$
D40

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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 $4s=20\sqrt{2}$ .

Question 3

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

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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.

Practice 57 Lines, angles, and polygons questions in the app

Lines, angles, and polygons — ACT practice questions

Sample questions

More ACT topics

Mathematics