In the figure below, line m is parallel to line n. If m∠3 = (12x + 5) degrees and m∠5 = (30x - 35) degrees: a) Solve for x.

b)Find the angle measure of all eight angles below.

Step-by-step explanation:

a) m∠3 + m∠5 = 180° (interior angles on the same side of the transversal)

(12x + 5) + (30x - 35) = 180°

12x + 5 + 30x - 35 = 180°

42x - 30 = 180°

42x = 180° + 30°

42x = 210°

x = 210/42 (by transposing)

x = 5°

By substituting the value of x,

m∠3 = 12x + 5 = 12(5) + 5 = 60 + 5 = 65°

m∠5 = 30x - 35 = 30(5) - 35 = 150 - 35 = 115°

m∠3 = m∠6 = 65° (alternate interior angles are equal)

m∠4 = m∠5 = 115° (alternate interior angles are equal)

m∠5 = m∠8 = 115° (vertically opposite angles are equal)

m∠6 = m∠7 = 65° (vertically opposite angles are equal)

m∠4 = m∠1  = 115° (vertically opposite angles are equal)

m∠3 = m∠2 = 65° (vertically opposite angles are equal)

m∠5 = m∠8 = m∠4 =m∠1 = 115°

m∠3 = m∠2 =m∠6 = m∠7 = 65°

Hope you understood!!

step-by-step explanation:

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step-by-step explanation: