Question

The angles of a quadrilateral are (p+25)°, 2p°,(2p−15)° and (p+20)° . What is the value of the largest angle? a)105° b)110° c)115° d)135°​

Answer 1

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°.

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

$\\ : \implies \sf \: 6p + 30 = {360}^{ \circ}$

$\\ : \implies \sf \: 6p = 360 - 30$

$\\ : \implies \sf \: 6p = 330$

$\\ : \implies \sf \: p = \dfrac{330}{6}$

$\\ : \implies{\underline{\boxed{\pink{\mathfrak{p = 55}}}}} \: \bigstar$

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

Answer 2

Answer:

Given :-

• Measure of all angles = (p +25), 2p,(2p-15),(p+20)

To Find :-

Value of largest angle

Solution :-

As we know that sum of all interior angles of a quadraliteral is 360°.

$\tt \mapsto \:(p + 25) + (2p) + (2p - 15) + (p + 20) = 360$

$\tt \implies \: 6p + (25 - 15) + 20 \: = 360$

$\tt \implies \: 6p + 10 + 20 = 360$

$\tt \implies \: 6p + 30 = 360$

$\tt \implies \:6p = 360 - 30$

$\tt \implies \: 6p = 330$

$\tt \implies \: p = \dfrac{330}{6}$

$\tt \implies \: p = 55$

Now,

Let's find angles

$\tt \implies \: (p + 25) = (55 + 25) = 80$

$\tt \implies \: 2p = 2(55) = 110$

$\tt \implies \: (2p - 15) = (2 \times 55 - 15) = 95$

$\tt \implies \: (p + 20) = (55 + 20) = 85$

Hence :-

Correct Option B