Question

5.
The measure of an angle of a quadrilateral is
120°. The measures of remaining angles are
equal, then find the measure of each angle.​

Answer 1

Answer:

Measure of each of the remaining angles is 80°.

Step-by-step explanation:

Quadrilateral has four vertices.  From any one vertex we can draw only one diagonal, producing two triangles.  Each of such triangles have the sum of its angles = 180°.  Therefore, the sum of the angles of the quadrilateral = 2 x 180°.

Now, one the four angles is 120°.  Therefore, the sum of the remaining three angles = 2 x 180° - 120° = 240°.

Since, remaining three angles are equal in measure, each of these angles = $\frac{1}{3} . 240$  = 80°

Answer 2

$\huge\underline{\bf\color{lime}{Answer :-}}$

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$\large\underline{\bf\color{darkgrey}{ Given :-}}$

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• The measure of an angle of a quadrilateral is 120°

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• Measures of remaining angles are equal

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$\large\underline{\red{\bf To \: Find :-}}$

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• The measure of other angles

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$\large\underline{\orange{\bf Solution :-}}$

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We know that a quadrilateral has 4 angles , so remaining number of angles are 3

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• Let the other 3 angles be "x"

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Also we know that sum of all angles of a quadrilateral is 360°

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Hence ,

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$\bf \footnotesize{ Angle \: 1 + Angle \: 2 + Angle \: 3 + Angle \: 4 = 360° }$

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➜ 120° + x + x + x = 360°

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➜ 120° + 3x = 360°

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➜ 3x = 360° - 120°

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➜ 3x = 240°

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➨ x = 80°

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• Hence the measure of other 3 angles is 80°

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