Uisbg multiple line and angle theorems, the values of each of the 14 angles are given.
Using the geometry theorems :
1.)
∠2 is a right angle = 90°
2.)
∠1 + ∠2 + ∠3 = 180° (sum of angle on a straight line)
90 + ∠1 + 54° = 180°
∠1 = (180 - 144) = 36°
(∠2 and ∠5) ; (∠3 and ∠6) ; (∠1 and ∠4) are vertically opposite ;
Hence,
∠4 = 36°
∠5 = 90°
∠6 = 54°
∠3 = ∠8 = 54° (corresponding angles)
∠9 + ∠8 = 180° (sum of angle on a straight line)
∠9 = (180 - 54) =126°
∠7 = ∠9 = 126° (vertically opposite angles)
∠8 = ∠10 = 54° (vertically opposite angles)
∠4 = ∠13 = 36° (corresponding angles )
∠12 + ∠13 = 180° (sum of angle on a straight line)
∠12 = (180 - 36) =126°
∠11 = ∠13 = 36° (vertically opposite angles)
∠12 = ∠14 = 126° (vertically opposite angles)
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