Question

Find the value of each indicated angle?

Answer 1

Answer:

1 x=91

2 x=98

3 x=180-118=62

4 x=53

5 x=180-122=58

6 x=88

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Answer 2

The values of x in the given 6 figures are 89, 98, 62, 53, 58, and 88 respectively.

Let us follow the convention of naming the angles as angles A, B, C, and D for the angles above and below the first parallel line and angles E, F, G, and H for the second parallel line.

1.  Value of angle x is 89 degrees.

Given : Angle D = 91

To Find : Angle F = x

Solution :

Angle D and F are a pair of adjacent angles i.e. same side interior angles and thus sum to 180.

                       $91 + x = 180$

                       $x = 180 - 91$

                       $x = 89$

2.  Value of angle x is 98 degrees.

Given : Angle G = 98

To Find : Angle B = x

Solution :

Angle C and G are a pair of corresponding angles i.e. same side of traversal and thus are the same. Also, Angle B and C  are vertically opposite and the same. So,

                       $x = B = C = G$

                       $x = 98$

3.  Value of angle x is 62 degrees.

Given : Angle A = 118

To Find : Angle G = x

Solution :

Angles C and G are a pair of corresponding angles as above and are the same. Angles A and C are complementary angles and should sum to 180.

                       $118 + x = 180$

                       $x = 180 - 118$

                        $x = 62$

4.  Value of angle x is 53 degrees.

Given : Angle C = 53

To Find : Angle F = x

Solution :

Angles C and F are a pair of alternate interior angles forming a "Z" and thus are the same.So,

                       $x = F = C$

                       $x = 53$

5.  Value of angle x is 58 degrees.

Given : Angle E = 122

To Find : Angle C = x

Solution :

Angles C and E are the interior adjacent angles on the same side of the traversal and thus are complementary to 180. So,

                       $x + 122 = 180$

                       $x = 180 - 122$

                       $x = 58$

6.  Value of angle x is 88 degrees.

Given : Angle A = 88

To Find : Angle H = x

Solution :

Angles A and E are the same as they are corresponding angles. Also angles E and H are the same as they are vertically opposite angles. Thus,

                       $x = H = E = A$

                       $x = 88$

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