Question

In a parallelogram ABCD, if A = (2x + 35)º and C = (3x - 5)º.
Find : the value of x (ii) measure of each angle of ABCD.
Hint: ZA = 2C, B = D and ZA + B + 2C + D = 360°.] )​

Answer 1

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Given Information :

• ABCD is a parallelogram.

• Measure of ∠A is (2x + 35)°

• Measure of ∠C is (3x – 5)°

To calculate :

• Value of x.

• Measure of each angle of ABCD.

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Clarification :

Here, we are provided that ABCD is a parallelogram. Measure of ∠A is (2x + 35)° and measure of ∠C is (3x – 5)°. We are asked to calculate the value of x and measure of each angle. Basically, we need to apply the properties of parallelogram and a quadrilateral to find the value of x and measure of each angle.

In order to find the value of x, we'll apply the property of a parallelogram that is, opposite angles of a parallelogram are equal.

And, in order to find the measure of each angle of ABCD, we'll apply two properties that are,opposite angles of a parallelogram are equal and angle sum property of a quadrilateral.

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☀ Angle sum property of quadrilateral :

• Sum of all interior angles of a quadrilateral = 360°

So, let's commence the steps!

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Explication of steps :

★ Finding value of x :

As we know that,

• Opposite angles of a parallelogram are equal. So,

➝ ∠A = ∠C

We are given that,

• ∠A = (2x + 35)°

• ∠C = (3x – 5)°

Substituting values,

➝ 2x + 35 = 3x – 5

➝ 35 + 5 = 3x – 2x

➝ $\boxed {\sf \red{40 = x} }$

❝ Therefore, value of x is 40. ❞

† Finding measure of each angle of ABCD :

We have,

• ∠A = (2x + 35)°

• ∠C = (3x – 5)°

As we found the value of x, so now substitute the value of x in the expression of measure of ∠A and ∠C to find the measure of ∠A and C.

➝ ∠A = (2x + 35)°

➝ ∠A = {2(40) + 35}°

➝ ∠A = {80 + 35}°

➝ $\boxed {\sf \red{\angle A = 115^\circ} }$

As we know that,

• Opposite angles of a parallelogram are equal. So,

➝ ∠A = ∠C

➝ $\boxed {\sf \red{\angle C = 115^\circ} }$

Now, we have to find the measure of ∠B and ∠D.

➝ ∠B = ∠D [Opposite angles of a parallelogram are equal]

Let us assume ∠B and ∠D as y° each as they are equal.

➝ ∠B = y°

➝ ∠D = y°

We know that,

Angles sum of a quadrilateral is 360°. So,

➝ ∠A + ∠B + ∠C + ∠D = 360°

➝ 115° + y° + 115° + y° = 360°

➝ 230° + 2y° = 360°

➝ 2y° = 360° – 230°

➝ 2y° = 130°

➝ y° = $\sf { \cancel { \dfrac{130^\circ}{2} }}$

➝ y° = 65°

Therefore,

➝ $\boxed {\sf \red{\angle B = 65^\circ} }$

➝ $\boxed {\sf \red{\angle D = 65^\circ} }$

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