Question

2. The
angles a Quadrilates al are in
A.p with d=10'. find the angles.

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Answer 1

Answer:

The angles of the quadrilateral are 75°, 85°, 95°, 105°.

Step-by-step-explanation:

Let the smallest angle of the quadrilateral be ( a - d ).

∴ The three angles are a, ( a + d ), ( a + 2d ).

We know that,

The sum of measures of angles of the quadrilateral is 360°.

∴ ( a - d ) + a + ( a + d ) + ( a + 2d ) = 360

⇒ a - d + a + a + d + a + 2d = 360

⇒ a + a + a + a - d + d + 2d = 360

⇒ 4a + 2d = 360

⇒ 2a + d = 180 - - - [ Dividing both sides by 2 ]

⇒ 2a + 10 = 180 - - - [ Given ]

⇒ 2a = 180 - 10

⇒ 2a = 170

⇒ a = 170 ÷ 2

⇒ a = 85

Now,

First angle = a - d

⇒ First angle = 85 - 10

⇒ First angle = 75°

Now,

Second angle = a

⇒ Second angle = 85°

Now,

Third angle = a + d

⇒ Third angle = 85 + 10

⇒ Third angle = 95°

Now,

Fourth angle = a + 2d

⇒ Fourth angle = 85 + 2 * 10

⇒ Fourth angle = 85 + 20

⇒ Fourth angle = 105°

∴ The angles of the quadrilateral are 75°, 85°, 95°, 105°.