Name: Kites and Rhombuses Formed by Four Points
Uploaded: 2019-07-19
Duration: 10 min 9 s
Description: What is the relationship between kites and rhombuses? Will you believe me if I tell you all the rhombuses are kites? Check out this video to understand the connection in detail!

Question

Find the measures of the lettered angles in the rhombus $M N P Q$ .

Accepted Answer

Given, $M N P Q$ is a rhombus.

In a rhombus, diagonals bisect each other perpendicularly.

$\Rightarrow ∠ Q O P = c = 90 °$

Similarly, $∠ P O N = ∠ N O M = ∠ M O Q = 90 ° . . . (1)$

From $(1)$ , it is clear that $△ M O N$ is a right triangle.

In $△ M O N$ ,

$∠ M O N + ∠ O M N + ∠ O N M = 180 °$ (Angle sum property of triangles)

$\Rightarrow ∠ O M N = 180 ° - 90 ° - 53 °$

$\Rightarrow ∠ O M N = 37 ° . . . . (2)$

In a rhombus, diagonals bisect the interior angles.

$\Rightarrow a = ∠ O M N = 37 ° . . . . . . . . (3)$

Similarly, $e = 53 °$

In a rhombus, opposite sides are parallel.

So, $Q M | | P N$ and $Q P | | M N$

$\Rightarrow d = a$ (alternate angles)

$\Rightarrow d = 37 °$

Also, $b = 53 °$ (alternate angles)

Hence, the measure of the lettered angles are $37 °, 53 °, 90 °, 37 °$ and $53 ° .$

Find the measures of the lettered angles in the rhombus $M N P Q$ .

Important Questions on Rectilinear Figures

Learn and Prepare for any exam you want !

Find the measures of the lettered angles in the rhombus MNPQ.

Important Questions on Rectilinear Figures

Learn and Prepare for any exam you want !

Find the measures of the lettered angles in the rhombus $M N P Q$ .