Junior Secondary · Mathematics

Geometry: Practice Questions

5 multiple-choice questions marked as you go, and 5 written questions with worked solutions. All on Geometry.

10 questions22 marksFree, no account

Question 1

1 mark

A square has all sides equal and all interior angles equal to $$90^\circ$$. If one of its diagonals is drawn, what is the measure of the angle formed between this diagonal and one of the sides of the square?

Question 2

1 mark

Two parallel lines, $L_1$ and $L_2$, are intersected by a transversal. If two consecutive interior angles measure $(2x + 10)^\circ$ and $(3x - 50)^\circ$, find the value of $x$.

Question 3

1 mark

The interior angles of a convex polygon form an arithmetic progression. The smallest angle is $ 120^\circ $ and the common difference is $ 5^\circ $. Find the number of sides of this polygon.

Question 4

1 mark

Calculate the measure of one interior angle of a regular octagon.

Question 5

1 mark

In a regular polygon, the sum of the interior angles is $1080^\circ$. How many sides does this polygon have?

Question 6

2 marks

If two angles are complementary and one of the angles measures $$30^\circ$$, what is the measure of the other angle?

Write your answer out first, then check it against the worked solution.

Question 7

5 marks

In a regular $n$-sided polygon, each interior angle is $8$ times the size of each exterior angle. If the number of sides of this polygon is increased by $k$, the ratio of each interior angle to each exterior angle becomes $11:1$. Find the value of $k$.

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Question 8

2 marks

What type of quadrilateral has exactly one pair of parallel sides?

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Question 9

4 marks

A quadrilateral $$ABCD$$ has interior angles given by the following expressions:

$$\angle A = (2x)^\circ$$
$$\angle B = (3x+10)^\circ$$
$$\angle C = (x+40)^\circ$$
$$\angle D = (4x-10)^\circ$$

(a) Find the value of $$x$$.

(b) Calculate the measure of each interior angle of the quadrilateral.

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Question 10

4 marks

In the figure, the straight line $AB$ is parallel to the straight line $CD$. Point $P$ lies between the parallel lines. Given that $\angle ABP = 35^\circ$ and $\angle CDP = 60^\circ$.

(a) By drawing an auxiliary straight line $XY$ passing through $P$ and parallel to $AB$, find the measure of $\angle BPD$. Show your steps clearly and state the geometric reasons.

(b) If $BP$ is extended to a point $Q$ such that $B, P, Q$ are collinear, find the measure of $\angle DPQ$.

Write your answer out first, then check it against the worked solution.

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