Ex 3.1, 7 (b) Find x + y + z + w Given, ∠ PAB = z ∠ BAD = 60° ∠ QBC = w ∠ BCD = 120° ∠ DCR = x ∠ADC = 80° ∠ ADS = y
Now,
ABCD has 4 sides
So, it’s a quadrilateral
And we know that
Sum of angles of Quadrilateral = 360°
∠BAD + ∠ABC + ∠BCD + ∠ADC = 360°
60° + ∠1 + 120° + 80° = 360°
260° + ∠1 = 360°
∠1 = 360° − 260°
∠ 1 = 100°
PAD is a line segment,
∠PAB + ∠BAD = 180°
z + 60° = 180°
z = 180° − 60°
z = 120°
QBA is a line segment,
∠ABC + ∠QBC = 180°
∠1 + w = 180°
100 + w = 180°
w = 180° − 100°
w = 80°
BR is a line segment,
∠DCR + ∠BCD = 180°
x + 120° = 180°
x = 180° − 120°
x = 60°
CS is a line segment
∠ADS + ∠ADC = 180°
y + 80° = 180°
y = 180° − 80°
y = 100°
Thus, x = 60° , y = 100° , w = 80° , z = 120°
∴ x + y + z + w = 60° + 100° + 120° + 80°
= 360°

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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