Question

In a quadrilateral ABCD, ∠D is equal to 150° and ∠A = ∠B = ∠C. Find ∠A, ∠B and ∠C

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Answer 1

Answer:

A, B, C = 70°

Step-by-step explanation:

A+B+C+D=360°

but A, B, C are equal

A+A+A+150°=360°

3A+150°= 360°

3A= 360-150

3A= 210

A= 210/3

A= 70°

Answer 2

⇒ Final Answer:

∠A = ∠B = ∠C = 70°

⇒ Given:

A quadrilateral ABCD with ∠D equal to 150°.

∠A = ∠B = ∠C

⇒ To Find:

The value of ∠A, ∠B and ∠C.

⇒ Solution:

The basic concept that we must know while solving this question is the angle sum property of a quadrilateral. According the angle sum property of a quadrilateral, the sum of all the four angles is always equal to 360°.

Here, it is given that:

∠D = 150°

Let ∠A, ∠B and ∠C have the value x.

According to the angle sum property of a quadrilateral:

Sum of all angles = 360°

150° + x + x + x = 360°

150° + 3x = 360°

3x = 360 - 150

3x = 210

$\sf{x=\dfrac{210}{3}}$

So, x = 70

∴ The value of x is 70c.

∠A = ∠B = ∠C = x

So:

∠A = 70°

∠B = 70°

∠C = 70°

⇒ Verification:

As said earlier, the sum of all the angles of a quadrilateral must always be 360°.

LHS

= 150 + x + x + x

x = 70

= 150 + 70 + 70 + 70

= 220 + 140

= 360

RHS

= 360

LHS = RHS

Hence proved!