Mathematics: Given: ABCD ∥gram BK ⊥ AD , AB = 6, AK = 3 Find: m∠A, m∠B, m∠C, m∠D

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Given: ABCD ∥gram BK ⊥ AD , AB = 6, AK = 3 Find:

Ответ:

kami23arap5p78v

29.01.2022

Mathematics

m∠A 60°, m∠B= 120°, m∠C =60°, m∠D=120°

Step-by-step explanation:

$In\: ||^{gm} \: ABCD, \: BK\perp AD... (given) \\\therefore \angle BKA = 90\degree \\In\:\triangle BKA, \\\\\cos \angle A = \frac{AK}{AB}\\\\\cos \angle A = \frac{3}{6}\\\\\cos \angle A = \frac{1}{2}\\\\\cos \angle A = \cos 60\degree.. (\because \cos 60\degree = \frac{1}{2}) \\\\\huge \red {\boxed {\therefore \angle A = 60\degree}} \\$

Since, adjacent angles of a parallelogram are Supplementary.

$\therefore \angle A + \angle B = 180\degree \\\therefore 60\degree + \angle B = 180\degree \\\therefore \angle B = 180\degree - 60\degree\\\huge \purple {\boxed {\therefore \angle B = 120\degree}} \\$

Since, opposite angles of a parallelogram are congruent.

$\therefore \angle C = \angle A \\ \huge \red{\boxed {\therefore \angle C = 60\degree}} \\\\\therefore \angle D = \angle B \\ \huge \purple {\boxed {\therefore \angle D = 120\degree}} \\$

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Given: ABCD ∥gram BK ⊥ AD , AB = 6, AK = 3 Find: m∠A, m∠B, m∠C, m∠D

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