Geometry Homework 1 Quarter 1

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
--------------

2.  

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

  1. 61
  2. 11
--------------

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
--------------

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
--------------

5.  

In the diagram of ΔABC, , and mA = 70.

Find the measure of the vertex angle.

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

Figure 1

In the diagram, ACD is an exterior angle of ΔABC. If mB = 40, mA = 2x, and mACD = 3x, what is the value of x?

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

7.  

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

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

8.  

In the diagram, mA = x + 20, mB = 3x, and BCD is an exterior angle formed by extending  to point D, and mBCD = 120.

Find the value of x.

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

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
--------------
10.  

Which pairs of angles x and y are supplementary?

  1.   mx = 113 and my = 67
  2.   mx = 76 and my = 14
  3.   mx = 140 and my = 190
  4.   mx = 180 and my = 180
--------------

11.  

In the diagram: image ≅  image and mA = 80.

Find mC.

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

12.  

In the diagram, ACD is an exterior angle of ΔABC, mA = 3x, mACD = 5x, and mB = 50.

What is the value of x?

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

Figure 2

In the diagram of ΔABC, the measure of exterior angle BCD is 120° and mBAC = 50. Find mABC.

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

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
--------------

15.  

Figure 3

In the diagram of ΔABC, the measure of an exterior angle at C is 105 and mA = 35. Find mB.

1.   30       3.   70
2.   40       4.   90
--------------

Please submit your answers here.

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