5,051 views
28 votes
28 votes
Give proper explanation

Give proper explanation-example-1
User Deadboy
by
3.1k points

1 Answer

22 votes
22 votes

Answer:

a = 84°

b = 21°

c = 48°

Explanation:

Step 1.)

The first step is recognizing the angle of 75° is sticking out from a straight-line, PQ. That straight-line represents an angle of 180°

180°-75° = 105 = a° + b°

Step 2.)

We also know that the line RS is 180°. Therefore, it must be true that

75° + 4b° + b° = 180°

or simply

5b + 75 = 180°

Now solve for b. Subtract both sides by 75 and divide the right side by 5

5b = 105°

b = 21°

4b° = 4 x b = 4 x 21° = 84° = 4b°

Step 3)

Since we know that a + b = 105°, we use substitution to get:

a + 21° = 105

Now subtract both sides by 21

a = 84°

Now let's double check if a + b + 75 = 180

84 + 21 + 75 = 180 [check]

Step 4.)

Since we know that PQ is a straight-line that is 180°, we can say:

180° = 4b° + 2c°

Now substitute 4b with 84°

180° = 84° + 2c

Now solve by subtracting 84 from 180 and divide by 2, if needed.

96° = 2c°

48° = c°

Now double check

96° + 84° = 180° [check]

Therefore:

a = 84°

b = 21°

c = 48°

Hope that helps.

Don't forget to show some love and award stars!

User Viktor Sehr
by
3.0k points