angle in rectilinear figures

18.
ΔABD is an isos. Δ. AB = AD
Then, ∠B = ∠D

∠BAD + ∠B + ∠D = 180° (∠ sum of Δ)
(56° + 22°) + ∠B + ∠B =180°
∠B = 51°

∠ACD = ∠BAC + ∠B (ext. ∠ of Δ)
∠ACD = 56° + 51°
∠ACD = 107°


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19.
ΔABC is an isos. Δ with AB = AC.
Hence, ∠ACB = ∠ABC = 61°

∠ACD + ∠ACB = 180° (adj. ∠s on a st. line)
∠ACD + 61° = 180°
∠ACD = 119°


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20.
Sum of exterior angles of a regular hexagon = 360°

An exterior angle of a regular hexagon
= 360°/6
= 60°


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21.
∠FCB = ∠ABC (alt. ∠s, AB//CF)
∠FCB = 60°

∠DEF = 60° (given)

∠FCB = ∠DEF
Hence, BC // DE (corr. ∠s equal)


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22.
∠ADC + ∠CDE = 180° (adj. ∠s on a st. line)
∠ADC + 113° = 180°
∠ADC = 67°

Sum of int. ∠s of quadrilateral ABCD =360°
x + 85° + 78° + 67° = 360°
x = 130°