Write a letter to your brother telling him about a movie you have seen.
Answers
Answer:
x = 85°
∠C = 105°
Explanation:
In the ||gm ABCD,
∠B = (5x + 25)° and ∠D = (8x - 5)°
Find the value of ‘x’ and ∠C
Recall, the property of a ||gm.
Opposite angles are equal.
\rm \therefore \angle B = \angle D∴∠B=∠D
Solving for ‘x’ :-
\rm \implies \: (5x + 25)^{ \circ} = (8x - 5)^{ \circ}⟹(5x+25)
∘
=(8x−5)
∘
\rm \implies \: 5x + 25 = 8x - 5⟹5x+25=8x−5
\rm \implies \: 25 + 5 = 8x - 5x⟹25+5=8x−5x
\rm \implies \: 30 = 3x⟹30=3x
\rm \therefore \: x = {10}^{ \circ}∴x=10
∘
Therefore, the value of ‘x’ is 10°
Now
Recalling the property again,
Adjacent angles of a ||gm is equal to 180°
\rm \therefore \: \angle D + \angle C = {180}^{ \circ}∴∠D+∠C=180
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Where,
∠D = 8x - 5 = 8(10) - 5 = 75°
Substituting ∠D :-
\rm \implies \: 75^{ \circ} + \angle C = {180}^{ \circ}⟹75
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+∠C=180
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\rm \implies \: \angle C = {180}^{ \circ} - 75^{ \circ}⟹∠C=180
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−75
∘
\rm \implies \: \angle C = {105}^{ \circ}⟹∠C=105
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Hence, ∠C is 105°