Question

Measure of one angle of a rhombus is 50°, find the measures of remaining three angles.

Answer 1

Suppose ABCD is a rhombus.

Let m∠A = 50º

Opposite angles of a rhombus are congruentes.

∴ m∠C = m∠A = 50º and m∠B = m∠D

Now,

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.