Dhondoop's field has adjacent angles in the ratio 4:5. Find all the angles of his field.
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Solution:-
You have not mentioned the shape of the field. If it is in the shape of a parallelogram then the answer is as follows.
Suppose ABCD is a parallelogram in which ∠ B and ∠ C are adjacent angles.
Since ∠ B and ∠ C are adjacent interior angles formed by two parallel lines AB and DC
As we know that the sum of the two adjacent angles of a parallelogram is 180°.
∠ B + ∠ C = 180°
⇒ 4x + 5x = 180°
⇒ 9x = 180°
⇒ x = 180/9
⇒ x = 20°
So, ∠ B = 4*20 = 80°
and ∠ C = 5*20 = 100°
We know that the opposite angles of a parallelogram are equal.
So,
∠ D = ∠ B = 80°
And ∠ A = ∠ C = 100°
Answer.
You have not mentioned the shape of the field. If it is in the shape of a parallelogram then the answer is as follows.
Suppose ABCD is a parallelogram in which ∠ B and ∠ C are adjacent angles.
Since ∠ B and ∠ C are adjacent interior angles formed by two parallel lines AB and DC
As we know that the sum of the two adjacent angles of a parallelogram is 180°.
∠ B + ∠ C = 180°
⇒ 4x + 5x = 180°
⇒ 9x = 180°
⇒ x = 180/9
⇒ x = 20°
So, ∠ B = 4*20 = 80°
and ∠ C = 5*20 = 100°
We know that the opposite angles of a parallelogram are equal.
So,
∠ D = ∠ B = 80°
And ∠ A = ∠ C = 100°
Answer.
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