solid geometry - Angle

SOURCE:COMPETITION
Number of Problems: 14. : (Book)

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The degree measure of angle $A$ is

$ext{(A)} 20 qquad ext{(B)} 30 qquad ext{(C)} 35 qquad ext{(D)} 40 qquad ext{(E)} 45$

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8.

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Find the degree measure of an angle whose complement is 25% of its supplement.

$mathrm{(A) 48 } qquad mathrm{(B) 60 } qquad mathrm{(C) 75 } qquad mathrm{(D) 120 } qquad mathrm{(E) 150 }$

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9.

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The angles of quadrilateral $ABCD$ satisfy $angle A=2 angle B=3 angle C=4 angle D.$ What is the degree measure of $angle A,$ rounded to the nearest whole number?

$extbf{(A) } 125 qquad extbf{(B) } 144 qquad extbf{(C) } 153 qquad extbf{(D) } 173 qquad extbf{(E) } 180$

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10.

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Triangles $ABC$ and $ADC$ are isosceles with $AB=BC$ and $AD=DC$ . Point $D$ is inside triangle $ABC$ , angle $ABC$ measures 40 degrees, and angle $ADC$ measures 140 degrees. What is the degree measure of angle $BAD$ ?

$mathrm{(A)} 20qquad mathrm{(B)} 30qquad mathrm{(C)} 40qquad mathrm{(D)} 50qquad mathrm{(E)} 60$

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11.

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Suppose that $frac{2x}{3}-frac{x}{6}$ is an integer. Which of the following statements must be true about $x$ ?

$mathrm{(A)} ext{It is negative.}\qquadmathrm{(B)} ext{It is even, but not necessarily a multiple of 3.}\qquadmat...$

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12.

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In the given circle, the diameter $overline{EB}$ is parallel to $overline{DC}$ , and $overline{AB}$ is parallel to $overline{ED}$ . The angles $AEB$ and $ABE$ are in the ratio $4 : 5$ . What is the degree measure of angle $BCD$ ?

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$extbf{(A)} 120 qquad extbf{(B)} 125 qquad extbf{(C)} 130 qquad extbf{(D)} 135 qquad extbf{(E)} 140$

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13.

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Triangle $ABC$ has $AB=2 cdot AC$ . Let $D$ and $E$ be on $overline{AB}$ and $overline{BC}$ , respectively, such that $angle BAE = angle ACD$ . Let $F$ be the intersection of segments $AE$ and $CD$ , and suppose that $riangle CFE$ is equilateral. What is $angle ACB$ ?

$extbf{(A)} 60^circ qquad extbf{(B)} 75^circ qquad extbf{(C)} 90^circ qquad extbf{(D)} 105^circ qquad ex...$

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14.

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Point B is due east of point A. Point C is due north of point B. The distance between points A and C is $10sqrt 2$ , and $angle BAC= 45^circ$ . Point D is 20 meters due north of point C. The distance AD is between which two integers?

$extbf{(A)} 30 ext{and} 31 qquad extbf{(B)} 31 ext{and} 32 qquad extbf{(C)} 32 ext{and} 33 qquad extbf{...$

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