In quadrilateral LMNP, m∠L = m∠M = m∠N = 90°. Find m∠P. What type of quadrilateral is □LMNP?

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Solution

In quadrilateral LMNP, m $∠$ L = m $∠$ M = m $∠$ N = 90°
m $∠$ L + m $∠$ M + m $∠$ N + m $∠$ P = 90° (Sum of all the angles of a quadrilateral is 360°)
$\Rightarrow$ m $∠$ P = 360° – (m $∠$ L + m $∠$ M + m $∠$ N)
= 360° – (90° + 90° + 90°) = 90°
Therefore, m $∠$ P = 90°
All the angles of $□$ LMNP are 90^o .
Therefore, $□$ LMNP is a rectangle.

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