Question

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Answer 1

Question given :

In a quadrilateral PQRS , if angle P = 60° and angle Q : angle R : angle S = 2 : 3 : 7 find the measure of Angle S

Required answer :

Let the all angles of the Quadrilateral be 60 , 2x , 3x and 7x .

Now by angle sum property we have ,

= 60 + 2x + 3x + 7x = 360

= 12x = 360 - 60

= 12x = 300

= x = 300/12

= x = 25

So , angle Q = 2x = 50°

Angle R = 3x = 75°

Angle S = 7x = 175°

Answer 2

Given :

• Angle P = 60° and Angle Q : Angle R : Angle S = 2 : 3 : 7

To Find:

• Measure of Angle S

Required Solution :

Let the all angles of the Quadrilateral be 60 , 2x , 3x and 7x .

• So , As we all know, Sum of the angles of the Quadrilateral = 360°

$\sf \: ➟ \: 60 + (2x + 3x + 7x) = 360 \\ \\ ➟ \sf \: 12x = 360 - 60 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ ➟ \sf \: 12x = 300 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ ➟ \sf \: x = \frac{300}{12} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ ➟ \sf \: x ={ \underline{ \boxed{ \bf\bigstar{ \purple{25}}}}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\: \: \: \: \: \:$

• Hence, the value of x = 25°

So ,

• Angle Q = 2 × 25° = 50°
• Angle R = 3 × 25° = 75°
• Angle S = 7 × 25° = 175°