IMO Level 1- Mathematics Olympiad (SOF) Class 7: Questions 585 - 587 of 1022

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Question number: 585

» Practical Geometry - Lines and Angles

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MCQ▾

Question

In the figure (not drawn to scale), ABCD is a rectangle, . Find y.

Arc d Arc d: Semicircle through H and I Arc c Arc c: Semicircle through R and S Arc e Arc e: Semicircle through T and U Segment f Segment f: Segment [A, B] Segment g Segment g: Segment [B, C] Segment h Segment h: Segment [C, D] Segment i Segment i: Segment [D, A] Segment j Segment j: Segment [A, C] Segment k Segment k: Segment [D, B] Point A A = (7.11,1.05) Point A A = (7.11,1.05) Point A A = (7.11,1.05) Point B B = (7.11,4.54) Point B B = (7.11,4.54) Point B B = (7.11,4.54) Point C C = (4.31,4.54) Point C C = (4.31,4.54) Point C C = (4.31,4.54) Point D D = (4.31,1.05) Point D D = (4.31,1.05) Point D D = (4.31,1.05) Point E Point E: Intersection point of j, k Point E Point E: Intersection point of j, k Point E Point E: Intersection point of j, k 75â° text1_1 = “75â°” y text2 = “y” 35â° text1_2 = “35â°”

Image Made by a Rectangle ABCD in Which ∠CBE = 75 Degree

Showing an image made by a rectangle ABCD, so find x.

Choices

Choice (4) Response

a.

b.

c.

d.

Question number: 586

» Comparing Quantities

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MCQ▾

Question

What percent of 1 day is 36 minutes?

Choices

Choice (4) Response

a.

2.5%

b.

3.6%

c.

25%

d.

0.25%

Question number: 587

» Practical Geometry - Lines and Angles

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MCQ▾

Question

In the figure (not drawn to scale), AE, DCH and ACG are straight lines, and . Find x and y respectively.

Arc c Arc c: Semicircle through I and J Arc d Arc d: Semicircle through K and Q Arc e Arc e: Semicircle through R and S Segment f Segment f: Segment [A, B] Segment g Segment g: Segment [B, C] Segment i Segment i: Segment [A, E] Segment j Segment j: Segment [F, G] Segment k Segment k: Segment [A, G] Segment l Segment l: Segment [B, H] Segment h Segment h: Segment [C, D] Vector u Vector u: Vector [O, P] Vector u Vector u: Vector [O, P] Vector u_1 Vector u_1: Vector [O_1, P_1] Vector u_1 Vector u_1: Vector [O_1, P_1] Point A A = (4.86,0.52) Point A A = (4.86,0.52) Point A A = (4.86,0.52) Point B B = (7.17,2.46) Point B B = (7.17,2.46) Point B B = (7.17,2.46) Point C C = (5.46,2.48) Point C C = (5.46,2.48) Point C C = (5.46,2.48) Point E E = (8.6,0.52) Point E E = (8.6,0.52) Point E E = (8.6,0.52) Point F F = (2.84,3.88) Point F F = (2.84,3.88) Point F F = (2.84,3.88) Point G G = (5.91,3.9) Point G G = (5.91,3.9) Point G G = (5.91,3.9) Point H H = (9.48,2.46) Point H H = (9.48,2.46) Point H H = (9.48,2.46) Point D D = (3.37,2.48) Point D D = (3.37,2.48) Point D D = (3.37,2.48) x text1 = “x” y text1_1 = “y” 60â° text1_2 = “60â°”

Image Made by Some Lines Making Two Unknown Angles

Showing an image made by some lines making two unknown angles, so find angles x and y.

Choices

Choice (4) Response

a.

b.

c.

d.