Practice Questions
Test your shape and angle perception with these Euclidean geometry questions.
If two angles are complementary and one is double the other, what is the larger angle?
Complementary sum = $90^\circ$. $x + 2x = 90 \Rightarrow 3x = 90 \Rightarrow x = 30$. Larger angle = $2x = 60^\circ$.
Find the area of an equilateral triangle with side 10 cm.
Area of equilateral triangle = $(\sqrt{3}/4) \times \text{side}^2 = (\sqrt{3}/4) \times 100 = 25\sqrt{3}$.
What is the length of the longest rod that can be placed in a room of dimensions 12m x 9m x 8m?
Rod length = $\sqrt{L^2 + B^2 + H^2} = \sqrt{12^2 + 9^2 + 8^2} = \sqrt{144+81+64} = \sqrt{289} = 17$ m.
A circle is inscribed in a square of side 14 cm. What is the area of the circle?
The diameter of the inscribed circle = side of the square = 14 cm. So radius $r = 7 cm$. Area = $\pi r^2 = (22/7) \times 49 = 154$ cm².
In triangle ABC, if ∠A = 50° and ∠B = 60°, find ∠C. Also determine the type of triangle.
Sum of angles = 180°. $∠C = 180 - 50 - 60 = 70°$. All angles are less than 90°, so it is an acute triangle.
The exterior angle of a triangle is 120° and one interior opposite angle is 50°. Find the other interior opposite angle.
Exterior angle = sum of interior opposite angles. $120 = 50 + x \Rightarrow x = 70°$.
The sum of interior angles of a polygon is 1260°. Find the number of sides.
$(n-2) × 180 = 1260 \Rightarrow n-2 = 7 \Rightarrow n = 9$ sides.
In a triangle, the ratio of sides is 3:4:5. Determine the nature of the triangle.
$3^2 + 4^2 = 9 + 16 = 25 = 5^2$. Since it satisfies Pythagoras theorem, it is a right-angled triangle.
Two parallel lines are cut by a transversal. If one interior angle is 65°, find the corresponding and alternate interior angles.
Corresponding angle = same side = 65°. Alternate interior angle = same = 65°.
The radius of a circle is increased by 20%. By what percentage does the area increase?
New radius = $1.2r$. New area = $π(1.2r)^2 = 1.44πr^2$. Increase = $1.44 - 1 = 0.44 = 44\%$.
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