Points, Lines, Planes, and Angle Relationships: math test solutions, Grade 10 – download the PDF

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7 October 20267 October 2026

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Test solutions Grade 10 : Points, Lines, Planes, and Angle Relationships — Zyro the alien explorer of Planète Maths

Test solutions with the detailed point scale. Add up your points and spot what to review.

Suggested time: 45 minutes. Out of 20 points. Calculator allowed only when the problem says so.

Sommaire

1 Vocabulary / 3 pts

(a) Two points. (1 pt) (b) Three. (1 pt) (c) The segment has two endpoints and a finite length; the ray has one endpoint at \(A\) and extends forever through \(B\). (1 pt)

2 Segment addition / 3 pts

\((4x - 3) + (2x + 9) = 48\), so \(6x + 6 = 48\) and \(x = 7\). (1 pt) \(RS = 25\text{ cm}\) (1 pt) and \(ST = 23\text{ cm}\) (1 pt). Check: \(25 + 23 = 48\).

3 Coordinates / 4 pts

(a) \(\left(\dfrac{-2 + 10}{2}, \dfrac{-1 + 8}{2}\right) = (4, 3.5)\). (2 pts) (b) \(PQ = \sqrt{12^2 + 9^2} = \sqrt{225} = 15\) units. (2 pts)

4 Adding angles / 4 pts

(a) \(6x + 12 = 132\), so \(x = 20\). (2 pts) (b) \(44^\circ\), \(54^\circ\), \(34^\circ\); the sum is \(132^\circ\). (1 pt) (c) A bisector would make \(66^\circ\) with \(OA\). \(m\angle AOB = 44^\circ\) and \(m\angle AOC = 98^\circ\), so neither does. (1 pt)

5 Vertical angles / 3 pts

Vertical angles are equal: \(7x - 4 = 4x + 23\), so \(x = 9\). (1 pt) \(m\angle 1 = 7(9) - 4 = 59^\circ\). (1 pt) \(\angle 2\) forms a linear pair with \(\angle 1\): \(m\angle 2 = 180 - 59 = 121^\circ\). (1 pt)

6 Construction / 3 pts

Open the compass to more than half of \(AB\) (1 pt). With the same opening, draw arcs centered at \(A\) and at \(B\) that meet above and below the segment, then draw the line through those two points (1 pt). It meets \(\overline{AB}\) at its midpoint and is perpendicular to it. (1 pt)