Question

SOLVE THE FOLLOWING EQUATIONS
1. Simplify (x? – 5) (x + 5) + 25
1​

Answer 1

Answer:

Given :

Angles of a quadraliteral are (p + 25)°, 2p°, (2p - 15)° and (p + 20)°

To Find :

The value of largest angle

Solution :

The sum of all four interior angles of a quadraliteral is 360°.

\begin{gathered} \\ : \implies \sf \: (p+25) {}^{ \circ} + 2p {}^{ \circ} + (2p - 15) {}^{ \circ} + (p+20) {}^{ \circ} = {360}^{ \circ} \\ \\ \end{gathered}

:⟹(p+25)

∘

+2p

∘

+(2p−15)

∘

+(p+20)

∘

=360

∘

\begin{gathered} \\ : \implies \sf \: 6p + 30 = {360}^{ \circ} \\ \\ \end{gathered}

:⟹6p+30=360

∘

\begin{gathered} \\ : \implies \sf \: 6p = 360 - 30 \\ \\ \end{gathered}

:⟹6p=360−30

\begin{gathered} \\ : \implies \sf \: 6p = 330 \\ \\ \end{gathered}

:⟹6p=330

\begin{gathered} \\ : \implies \sf \: p = \dfrac{330}{6} \\ \\ \end{gathered}

:⟹p=

6

330

\begin{gathered} \\ : \implies{\underline{\boxed{\pink{\mathfrak{p = 55}}}}} \: \bigstar \\ \\ \end{gathered}

:⟹

p=55

★

Then the values of angles are ,

(p + 25)° = 55 + 25 = 80°

2p° = 55(2) = 110°

(2p - 15)° = 2(55) - 15 = 110 - 15 = 95°

(p + 20)° = 55 + 20 = 75°

Among the given angles of quadrilateral , 110° is largest angle.

Hence ,

The value of largest angle among the given angles of quadrilateral is 110°. So , Option(b) is the required answer