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solid geometry - Angle

For COMPETITION
Number of Total Problems: 14.
FOR PRINT ::: (Book)

Problem Num : 11

From : NCTM

Type: Calculation

Section:solid geometry

Theme:None
Adjustment# : 0

Difficulty: 2

Category Angle

Analysis

Solution/Answer

Problem Num : 12

From : AMC10B

Type:

Section:solid geometry

Theme:
Adjustment# : 0

Difficulty: 1

'
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 $BCD$ ?

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

Category Angle

Analysis

Solution/Answer
Answer:

Problem Num : 13

From : AMC10

Type:

Section:solid geometry

Theme:
Adjustment# : 0

Difficulty: 1

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

Category Angle

Analysis

Solution/Answer
Let $angle BAE = angle ACD = x$ .
$egin{align*}angle BCD &= angle AEC = 60^circ\ angle EAC + angle FCA + angle ECF + angle AEC &= angle EAC +...$
Since $frac{AC}{AB} = frac{1}{2}$ , $angle BCA = oxed{90^circ extbf{(C)}}$

Answer:

Problem Num : 14

From : AMC10B

Type:

Section:solid geometry

Theme:
Adjustment# : 0

Difficulty: 1

'
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?

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

Category Angle

Analysis

Solution/Answer
Answer:

Array ( [0] => 3006 [1] => 8155 [2] => 7913 [3] => 8177 ) 141 2