Question

Maths quadrilaterals error analysis

Answer 1

x = 53°

Explanation:

Before finding the error, let's know the properties of rhombus.

• All sides are equal.
• Opposite sides are parallel.
• Opposite angles are equal.
• Diagonals bisect each other at right angles.
• Diagonals bisect the angles of a rhombus.
• The sum of two adjacent angles is equal to 180 degrees.

In this case:

Let's the point of intersection of diagonal be O.

m∡ QRP = x

m∡ SQR = 37°

Since diagonals bisect each other at right angles.

So, we have m∡ QOR.

In right angled triangle QOR

m∡ QRP + m∡ SQR + m∡ QOR = 180°

Substitute the value.

`\sf x + 37^\circ +90^\circ = 180^\circ`

`\sf x = 180^\circ - 37^\circ -90^\circ`

`\sf x = 53^\circ`

Therefore, Value of x is 53°.