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Lines, angles, and polygons — ACT practice questions

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

What this topic is

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.

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 $(5x)^\circ$, $(3x)^\circ$, and $x^\circ$. What is the value of $x$?

A15✗ Not this oneB18✗ Not this oneC20✓ CorrectD30✗ Not this one

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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 2Mid

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

A$10\sqrt{2}$✗ Not this oneB20✗ Not this oneC$20\sqrt{2}$✓ CorrectD40✗ Not this one

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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 3Easier

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

A1✗ Not this oneB4✗ Not this oneC5✓ CorrectD10✗ Not this one

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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.

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