Question

Please answer me my questions and correct ​

Answer 1

$\color {red} </p><p>\Large \underline {\underline {Question \: :}}$

1. The angles of a quadrilateral are 86° amd 112°. The other two angles are of equal measure. The measure of each equal angle is ______.
2. In a quadrilateral PQRS, angle P = 50°, angle Q = 50°, angle R = 60°, then angle S = ______. This is a ______ (concave/convex) quadrilateral.

$\color {red} </p><p>\Large \underline {\underline {Answer \: :}}$

Answer 1 :

• Two angles of quadrilateral = 86° and 112°
• Other two are of equal measure.

Let the other two angle be x.

Sum of interior angles of quadrilateral = 360°

86 + 112 + x + x = 360

198 + 2x = 360

2x = 360 - 128

2x = 232

x = 232/2

x = 116

$\implies$ So, other two angles are of measure 116°.

Hence, the measure of each angle is 116°

Answer 2 :

• Angle P = 50°
• Angle Q = 50°
• Angle R = 60°
• Angle S =?

Let the angle S be x.

Sum of interior angle of quadrilateral = 360°

50 + 50 + 60 + x = 360

160 + x = 360

x = 360 - 160

x = 200

So, angle S = 200°. And this is a convex polygon.

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