Question

The measures of the interior angles of a quad are in AP with common difference 20 degree find the measure of each angle ​

Answer 1

Answer:

Let the angle be a - 3d, a - d, a + d, a + 3d

using angle sum property

a - 3d + a - d + a + d + a + 3d = 360

4a = 360

a = 90

now, common difference = 20

so, a - d - a + 3d = 20

2d = 20

d = 10.

so angles are 60, 80, 100, 120

Answer 2

Answer:

75⁰, 85⁰, 95⁰, 105⁰

Step-by-step explanation:

Given,

the angles of a quadrilateral are in A.P, whose common difference d=20 ⁰

let the first angle of the quadrilateral be a......eq(1)

hence second angle must be a+20 ⁰

….eq(2)

similarly,

third angle is a+20 ⁰+20⁰

=a+40 ⁰

….eq(3)

fourth angle is a+30 ⁰

…...eq(4)

now, we know that sum of all the angles of a quadrilateral must be 360 ⁰

hence

a+a+20 ⁰+a+40 ⁰ +a+30 ⁰ =360 ⁰

⟹4a+60 ⁰ =360 ⁰

⟹4a=360 ⁰ −60 ⁰

⟹4a=300 ⁰

a=75 ⁰

first angle.

now put value of a in eq(2). eq(3) and eq(4 we get)

second angle 75 ⁰ +10 ⁰ =85 ⁰

third angle 75 ⁰ +20 ⁰=95 ⁰

fourth angle 75 ⁰ +30⁰ =105 ⁰

hence the A.P for these angles is

75 ⁰,85 ⁰,95⁰,105⁰