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Question 1 of 10

1. Question

Find the value of \(a \) if the points $\left( {3, – 1} \right),\left( {5,5} \right),\left( {a, – 4} \right)$ are collinear. Note that collinear means that more than two points lie on the same straight line.

\(a = \)

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Question 2 of 10

2. Question

The perpendicular bisector of \(\left( {1,2} \right)\) and \(\left( {3,7} \right)\) is \(4x + 10y + A = 0\).

\(A = \)

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Question 3 of 10

3. Question

Two angles of a pentagon are right angles. The other three angles are all equal. Find the size of these angles.

\( ^\circ \)

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Question 4 of 10

4. Question

Which of the following is a regular quadrilateral?

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Question 5 of 10

5. Question

A certain quadrilateral has each angle \( 10^\circ \) greater than the previous one, except the smallest angle. How large is the smallest angle?

\( ^\circ \)

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Question 6 of 10

6. Question

Find \(\theta \), correcting to the nearest degree, if the area of the triangle is 16 cm^{2}.

\(\theta = \) degree(s)

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Hint

\(Area = \dfrac{1}{2}ab\sin C\)

Question 7 of 10

7. Question

Find \(\theta \), correcting to the nearest degree.

To calculate the height of a tree, Sarah measures the angle of elevation to the top as \(42^\circ \). She then walks 20 m closer to the tree and measures the angle of elevation as \(61^\circ \). Find the height of the tree.