Answer/Discussion on Basic Geometry

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Beginning Algebra
Answer/Discussion to Practice Problems
on Basic Geometry

Answer/Discussion to 1a
What is the complementary angle to 33 ?

Basically we need an angle that when we add it to 33 we get 90.

Let's set it up and solve it algebraically, letting x be the missing angle and see what we get:

*Complimentary angles sum up to be 90

The complimentary angle to 33 degrees is 57 degrees.

(return to problem 1a)

Answer/Discussion to 2a
What is the supplementary angle to 33 ?

Basically we need an angle that when we add it to 33 we get 180.

Let's set it up and solve it algebraically, letting x be the missing angle and see what we get:

*Supplementary angles sum up to be 180

The supplementary angle to 33 degrees is 147 degrees.

(return to problem 2a)

Answer/Discussion to 3a
Figure ABCD is congruent to figure EFGH

If B = 55, C = 45, and D = 30, what is the measure of G?

Since G corresponds with C and the figures are congruent, then G = C = 45 degrees.

If AD = 10, EF = 15, and BC = 12, what is the length of EH?

Since side EH corresponds to side AD and the figures are congruent,
then side EH = side AD = 10.

(return to problem 3a)

Answer/Discussion to 4a
Figure ABCDE is similar to figure FGHIJ.

A = 30,

C = 40, and

E = 50, what is the measure of

Since F corresponds to A and the figures are similar, then F = A = 30.

If AE = 10, FJ = 20, and BC = 40, what is the length of GH?

Since side GH corresponds to side BC and the figures are similar to each other, then GH and BC are in proportion to each other. Similarly, FJ and AE are in proportion to each other. When setting up the proportion, make sure that you set it up the same on both sides.

*Corresponding sides of similar figures
are in proportion to each other

*Cross multiply

Side GH = 80.

(return to problem 4a)

Answer/Discussion to 5a

Find 2 if 7 = 50 degrees.

Since 2 and 7 are alternate exterior angles and the two lines are parallel, then 2 = 7 = 50 degrees.

(return to problem 5a)

Answer/Discussion to 5b

Find 3 if 6 = 50 degrees.

Since 3 and 6 are alternate interior angles and the two lines are parallel, then 3 = 6 = 50 degrees.

(return to problem 5b)

Answer/Discussion to 5c

Find 1 if 5 = 130 degrees.

Since 1 and 5 are corresponding angles and the two lines are parallel, then 1 = 5 = 130 degrees.

(return to problem 5c)

Answer/Discussion to 5d

Find 4 if 6 = 50 degrees.

Since 4 and 6 are not alternate exterior, alternate interior or corresponding angles, they are not guaranteed to be equal.

However, since 2 and 4 make a straight angle (180 degrees) and 2 and 6 are corresponding angles (which means they are equal), we can find the measure of 4.

*Corresponding angles are =
*Straight angle = 180

4 = 130 degrees.

(return to problem 5d)

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