Question

In a quadrilateral mnpq, <M=48°,<N =80° and P is three times than <Q. Find<P. ​

Answer 1

`\boxed{ \rm\angle P = \tt174{ {}^ \circ} }`

Explanation:

Given,

• ∠M=48°
• ∠N = 80°
• ∠P = Three Times more than ∠Q.

In a quadrilateral.

To Find:

• ∠P

Solution:

We know that in quadrilateral MNPQ,

`\rm \: \boxed{ \rm ∠M +∠ N +∠ P+ ∠Q = 360 ^( \circ)}`

`\rm \implies \: 48 {}^ \circ + 80 {}^ \circ + \angle P + \cfrac{1}{3} \angle \: P = 360 {}^(\circ)`

`\rm \implies \angle P + \cfrac{1}{3}\angle P = 360 { {}^ \circ} - 48{ {}^ \circ} - 80 {{}^ \circ}`

`\implies \rm \: \cfrac{4}{3} \angle P = 232 {{}^ \circ}`

`\rm \: \implies \: \angle P = 232 {}^(\circ) * \cfrac{3}{4}`

`\rm \implies \: \angle P = 174{ {}^ \circ}`

Thus, ∠P will be 174° .