Question

Find the values of a, b and c.

Answer 1

Look at the picture.

Corresponding Angles are equal.

Alternate Angles are equal.

Consecutive Angles add up to 180°.

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3a and 45 are Consecutive Angles. Therefore

3a + 45 = 180    |subtract 45 from both sides

3a = 135      |divide both sides by 3

a = 45.

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(2c - 1) and 45 are Corresponding Angles. Therefore

2c - 1 = 45     |add 1 to both sides

2c = 46     |divide both sides by 2

c = 23.

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3a and (12b + 3) are Alternate Angles. Therefore

3(45) = 12b + 3

135 = 12b + 3     |subtract 3 from both sides

132 = 12b      |divide both sides by 12

b = 11.