Question

Find the value(s) of the unknown(s)
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Answer 1

Answer:

$a = 8 \: \: \: \: b = 19 \: \: \: \: c = 20 \: \: \: \: d = 70 \: \: \: \: e = 10 \: \: \: \: f = 29$

Step-by-step explanation:

$a) \: \: \: \: 2b = 38 \: \: \: (corresponding \: angles) \\ b = \frac{38}{2} = 19 \\ \\ a + 30 + (180 - 2b) = 180 \: \: \: \: (co \: interior \: angles) \\ \\ a + 30 - 2b = 0 \\ \\ a = 2b - 30 \\ a = 2 \times 19 - 30 \\ a = 38 - 30 \\ a = 8 \\ \\ \\ \\ \\7c = 140 \: \: \: \: (corresponding \: angles) \\ \\ c = \frac{140}{7} \\ \\ c = 20 \\ \\ \\ \\ 7c = 2d \\ 7 \times 20 = 2 \times d \\ d = \frac{7 \times 20}{2} \\ \\ d = 7 \times 10 \\ d = 70 \\ \\ \\ \\ 3e + 7e = 180 \: \: \: \: (co \: interior \: angles) \\ \\ 10e = 180 \\ \\ e = \frac{180}{10} = 18 \\ \\ \\ \\ 2f + 6 = 3f - 23 \\ 6 + 23 = 3f - 2f \\ 29 = f \\ f = 29$