Question

Find the value of a if a + 10, 3a + 10, 5a - 10 and 3a - 10 are the angles of a
quadrilateral. Also find the measure of each angle.​

Answer 1

Given :-

Angles of a quadrilateral are a + 10, 3a + 10, 5a - 10 and 3a - 10

We know that the sum of all four angles in quadrilateral is 360°

➡ (a + 10) + (3a + 10) + (5a - 10) + (3a - 10) = 360°

➡ a + 10 + 3a + 10 + 5a - 10 + 3a - 10 = 360°

➡ 12a = 360°

➡ a = 360/12

➡ a = 30°

Hence, all the angles of the quadrilateral are :-

• a + 10 = 30 + 10 = 40°

• 3a + 10 = 3(30) + 10 = 100°

• 5a - 10 = 5(30) - 10 = 140°

• 3a - 10 = 3(30) - 10 = 80°

VERIFICATION :-

= 40° + 100° + 140° + 80°

= 140° + 220°

= 360°

HENCE VERIFIED!

Answer 2

Answer:

Given,

(a+10)+(3a+10)+(5a-10)+(3a-10)=360

=> 12a + 20 -20 = 360

=> a = 360/12

=> a = 30

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