Advertisements
Advertisements
प्रश्न
Measure of one angle of a rhombus is 50°, find the measures of remaining three angles.
उत्तर
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.
संबंधित प्रश्न
In the following figure RISK and CLUE are parallelograms. Find the measure of x.
The measure of one angle of a parallelogram is 70°. What are the measures of the remaining angles?
All the angles of a quadrilateral are equal to each other. Find the measure of each. Is the quadrilateral a parallelogram? What special type of parallelogram is it?
Which of the following statement is true for a rhombus?
Two of its angles are at right angles
ABCD is a rhombus. If ∠ACB = 40°, find ∠ADB.
One side of a rhombus is of length 4 cm and the length of an altitude is 3.2 cm. Draw the rhombus.
In a rhombus PQRS if PQ = 7.5 cm then find QR. If ∠QPS = 75° then find the measure of ∠PQR and ∠SRQ.
Diagonals PR and QS of a rhombus PQRS are 20 cm and 48 cm respectively. Find the length of side PQ.
Lengths of diagonals of a rhombus ABCD are 16 cm and 12 cm. Find the side and perimeter of the rhombus.
A rhombus is a parallelogram in which ______ sides are equal.
