What is the measure of a straight angle?
Answer: B
A straight angle is the angle formed by a straight line - half a full turn.
\[ \frac{360^{\circ}}{2} = 180^{\circ} \]
A right angle is a quarter turn (90°) and a complete angle a full turn (360°).
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If two angles are complementary, their sum is:
Answer: B
Complementary angles add to a right angle.
\[ \angle A + \angle B = 90^{\circ} \]
Angles adding to 180° are supplementary instead - the pair most often confused with this one.
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What is the sum of the interior angles of a triangle?
Answer: B
The three interior angles of any triangle add to a straight angle.
\[ \angle A + \angle B + \angle C = 180^{\circ} \]
This holds for every triangle, however stretched - it follows from drawing a line through one vertex parallel to the opposite side.
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A polygon with 8 sides is called a/an:
Answer: C
Polygons are named by their number of sides: hexagon 6, heptagon 7, octagon 8, nonagon 9.
The prefix octa- means eight, as in octave and octopus.
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Two angles of a triangle are 50° and 70°. What is the measure of the third angle?
Answer: B
\[ \angle C = 180^{\circ} - (50^{\circ} + 70^{\circ}) \]
\[ = 180^{\circ} - 120^{\circ} = 60^{\circ} \]
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If a transversal intersects two parallel lines, then the corresponding angles are:
Answer: A
When a transversal cuts two parallel lines, corresponding angles - those in matching positions at the two intersections - are equal.
Alternate angles are also equal, while co-interior angles are supplementary. Only the last pair adds to 180°.
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What is the measure of each interior angle of a regular hexagon?
Answer: D
The formula for the measure of an interior angle of a regular n-sided polygon is \(\frac{(n-2) \times 180°}{n}\).
For a hexagon, n=6.
Angle = \(\frac{(6-2) \times 180°}{6} = \frac{4 \times 180°}{6} = 4 \times 30° = 120°\).
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In a right-angled triangle, the lengths of the two legs are 6 cm and 8 cm. What is the length of the hypotenuse?
Answer: A
We use the Pythagorean theorem for a right-angled triangle: \(a^2 + b^2 = c^2\), where a and b are the legs and c is the hypotenuse.
\(6^2 + 8^2 = c^2\)
\(36 + 64 = c^2\)
\(100 = c^2\)
\(c = \sqrt{100} = 10\) cm.
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The supplement of an angle is 110°. Find the angle.
Answer: B
Supplementary angles add to 180°.
\[ \theta = 180^{\circ} - 110^{\circ} = 70^{\circ} \]
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How many diagonals does a pentagon have?
Answer: B
A polygon with \( n \) sides has
\[ \frac{n(n-3)}{2} \text{ diagonals} \]
\[ \frac{5(5-3)}{2} = \frac{10}{2} = 5 \]
Each vertex joins to all but itself and its two neighbours, and the division by 2 avoids counting each diagonal from both ends.
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