Geometry Homework 1 Quarter 1

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1.  

The measures of the three angles of a triangle are represented by x, 3x, and x + 30. Find the value of x.

1.   15       3.   42
2.   30       4.   65
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2.  

If the hypotenuse of a right triangle is 6 and one leg is 5, the other leg is

  2. 61
  4. 11
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3.  

Find the number of degrees in the measure of the base angle of an isosceles triangle whose vertex angle measures 70°.

1.   10       3.   70
2.   55       4.   180
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4.  

A child who is 4 feet tall casts a 6-foot shadow at the same time that a nearby tree casts a 30-foot shadow. What is the height of the tree?

1.   10 feet       3.   30 feet
2.   20 feet       4.   40 feet
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5.  

In the diagram of ΔABC, , and m∠A = 70.

Find the measure of the vertex angle.

1.   30       3.   70
2.   40       4.   110
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6.  

Figure 1

In the diagram, ∠ACD is an exterior angle of ΔABC. If m∠B = 40, m∠A = 2x, and m∠ACD = 3x, what is the value of x?

1.   40       3.   8
2.   28       4.   20
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7.  

If two angles of a triangle each measure 70°, the triangle is described as

1.   right       3.   obtuse
2.   scalene       4.   isosceles
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8.  

In the diagram, m∠A = x + 20, m∠B = 3x, and ∠BCD is an exterior angle formed by extending  to point D, and m∠BCD = 120.

Find the value of x.

1.   10       3.   35
2.   25       4.   40
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9.  

The length of the hypotenuse of a right triangle is 20 centimeters and the length of one leg is 12 centimeters. The length of the other leg is:

1.   8 cm       3.   32 cm
2.   16 cm       4.   36 cm
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10.  

Which pairs of angles x and y are supplementary?

  1.   m∠x = 113 and m∠y = 67
  2.   m∠x = 76 and m∠y = 14
  3.   m∠x = 140 and m∠y = 190
  4.   m∠x = 180 and m∠y = 180
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11.  

In the diagram: image ≅  image and m∠A = 80.

Find m∠C.

1.   10       3.   40
2.   20       4.   80
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12.  

In the diagram, ∠ACD is an exterior angle of ΔABC, m∠A = 3x, m∠ACD = 5x, and m∠B = 50.

What is the value of x?

1.   25       3.   60
2.   30       4.   100
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13.  

Figure 2

In the diagram of ΔABC, the measure of exterior angle BCD is 120° and m∠BAC = 50. Find m∠ABC.

1.   20       3.   40
2.   30       4.   70
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14.  

If the angles of a triangle are represented by x, 3x + 20, and 6x, the triangle must be

1.   obtuse       3.   acute
2.   right       4.   isoceles
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15.  

Figure 3

In the diagram of ΔABC, the measure of an exterior angle at C is 105 and m∠A = 35. Find m∠B.

1.   30       3.   70
2.   40       4.   90
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Please submit your answers here.

docs.google.com/a/archimedesacademy.org/spreadsheet/viewform

 

 

 


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