Measure of One Angle of a Rhombus is 50° .Find the Measures of Remaining Three Angles. - SSC (English Medium) Class 8 - Mathematics
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Measure of one angle of a rhombus is 50° .find the measures of remaining three angles.
Suppose ABCD is a rhombus.
Let m∠A = 50º.
Opposite angles of a rhombus are congruent.
∴ m∠C = m∠A = 50º and m∠B = m∠D
m∠A + m∠B + m∠C + m∠D = 360º
∴ 50º + m∠B + 50º + m∠D = 360º
⇒ m∠B + m∠D = 360º − 100º = 260º
⇒ 2 m∠B = 260º (m∠B = m∠D)
⇒ m∠B = `(260°)/2` = 130°
∴ m∠D = m∠B = 130º
Thus, the measures of the remaining angles of the rhombus are 130º, 50º and 130º.
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Solution Measure of One Angle of a Rhombus is 50° .Find the Measures of Remaining Three Angles. Concept: Some Special Parallelograms - Concept of Rhombus.