Math Quiz -Geometry Report a question What's wrong with this question? You cannot submit an empty report. Please add some details. Math Quiz -Geometry Covering: geometric concepts such as lines, angles, triangles, quadrilaterals, circles, and various coordinate geometry topics, including the distance formula, midpoint formula, and slope. 1 / 5 1. If the ratio of the measures of two complementary angles is 3:2, what is the measure of the smaller angle? a) 36Â° b) 45Â° c) 54Â° d) 62Â° Complementary angles are angles whose measures add up to 90Â°. Let's call the measures of the two complementary angles 3x and 2x. Thus, the equation can be written as: 3x + 2x = 90 5x = 90 Dividing both sides by 5 to solve for x: x = 18 Now we substitute x back into 2x, which represents the measure of the smaller angle: 2(18) = 36 So, the measure of the smaller angle is 36Â°. The correct answer is A) 36Â°. 2 / 5 2. In triangle ABC, angle A is 90 degrees, AB = 5, and AC = 12. Find the length of BC. a) 7 b) 11 c) 13 d) 15 Since angle A is 90 degrees, triangle ABC is a right-angled triangle with the right angle at vertex A. We can use the Pythagorean Theorem (aÂ² + bÂ² = cÂ²) to find the length of BC, where a and b are the two legs of the right-angled triangle and c is the hypotenuse. In triangle ABC, a = AB = 5, and b = AC = 12. We have to find the length of the hypotenuse BC. 5Â² + 12Â² = cÂ² 25 + 144 = cÂ² 169 = cÂ² Taking the square root of both sides: c = 13 So, the length of BC is 13. The correct answer is C) 13. 3 / 5 3. Two concentric circles share the same center, and the radius of the smaller circle is 6. If the area of the annulus (the region between the two circles) is 42Ï€, what is the radius of the larger circle? a) âˆš42 b) âˆš78 c) âˆš114 d) 12 Let r be the radius of the larger circle. The area of the annulus is the difference between the areas of the larger and the smaller circles. area_annulus = Ï€(rÂ²) - Ï€(6Â²) 42Ï€ = Ï€(rÂ²) - 36Ï€ Adding 36Ï€ to both sides and factoring out Ï€, we get: 78Ï€ = Ï€(rÂ²) Dividing both sides by Ï€: 78 = rÂ² Taking the square root of both sides: r = âˆš78 So, the radius of the larger circle is âˆš78. The correct answer is B) âˆš78. 4 / 5 4. What is the circumference of a circle with a diameter of 10 inches? a) 5Ï€ b) 10Ï€ c) 20Ï€ d) 25Ï€ To find the circumference of a circle, we can use the formula: Circumference = Ï€ Ã— diameter Given the diameter of the circle is 10 inches, we have: Circumference = Ï€ Ã— 10 So, the circumference of the circle is 10Ï€ inches. The correct answer is B) 10Ï€. 5 / 5 5. What is the length of the diagonal of a square with side length 8? a) 64 b) 8âˆš2 c) 16 d) 16âˆš2 To find the length of the diagonal of a square, we can use the Pythagorean theorem, as the diagonal divides the square into two congruent right triangles. Let d represent the length of the diagonal and s represent the side length of the square. In each right triangle, the legs are of length s, and the hypotenuse is of length d. According to the Pythagorean theorem: sÂ² + sÂ² = dÂ² Given that the side length of the square is 8, we have: 8Â² + 8Â² = dÂ² 64 + 64 = dÂ² 128 = dÂ² Taking the square root of both sides: d = âˆš128 = 8âˆš2 So, the length of the diagonal is 8âˆš2. The correct answer is B) 8âˆš2. Your score is 0% Restart Quiz