Question

Find the unknown angles a and b in each of the following figures. ​

Answer 1

b) Sum of all angles of a quadrilateral = 360°

angle P + angle Q + angle R + angle S = 360°

50° + a + 100° + a = 360°

2a = 360° - 150° = 210°

a = 210°/2

a = 105°

e) Sum of all angles of a quadrilateral = 360°

angle A + angle B + angle C + angle D + angle E = 360°

90° + 90° + a + a + a = 360°

3a = 360° - 180°

a = 180°/3

a = 60°

Hope it helps ❤️

Answer 2

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Solution:-

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Figure :-1

Sum of all the angles in quadrilateral is 360 °

P+R+Q+S= 360°

50°+100+Q+S=360°

150°+Q+S=360°

Q+S=360°-150°

Q+S=210°

We know Q=S ( taken as x)

$2x = 210 \\ x = \frac{210}{2} \\ x = 105$

Therefore S and Q = 105°

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Figure:- 2

Sum of all the angles in Pentagon is 540°

A+B+E+D+C= 540°

90°+90°+E+D+C=540°

180°+E+D+C=540°

E+D+C=540°-180

E+D+C=360°

We know E=D=C (taken as x)

$3x = 360 \\ x = \frac{360}{3} \\ x = 120$

Therefore E , D and C= 120°

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