Question

In parallelogram ABCD measure of angle A is three times the measure of angle B. Find the measure of angle C and angle D​

Answer 1

$\Large {\underline { \sf {Clarification :}}}$

Here, we are given that ABCD is a parallelogram, in which $\angle$ A is three times the measure of $\angle$ B. We have to find the measure of $\angle$ C & $\angle$ D.

In order to find the measure of $\angle$ C and $\angle$ D, we'll use 2 important properties here,

• Angle sum property of a quadrilateral

$\longmapsto$ Angle sum property of a quadrilateral states that the sum of all the angles of a quadrilateral is 360°. As a parallelogram is a quadrilateral, so sum of all the angles of a parallelogram is 360°.

• Opposite angles of a parallelogram are equal.

$\Large {\underline { \sf {Explication \: of \: Steps :}}}$

We have,

• ABCD is a Parallelogram.
• Measure of $\angle$ A is three times of $\angle$ B.

As per the question, we have to find out :

• $\angle$ C = ?
• $\angle$ D = ?

According to the question,

Let the measure of $\angle$ B be x°. So, according to the question,

$\longrightarrow$ $\angle$ A = 3 × Measure of $\angle$ B

$\longrightarrow$ $\angle$ A = 3x°

We know that,

★ Opposite angles of a parallelogram are equal.

So,

$\longrightarrow$ $\angle$ A = $\angle$ C

$\longrightarrow$ $\angle$ B = $\angle$ D

• $\angle$ A = 3x°
• $\angle$ B = x°
• $\angle$ C = 3x°
• $\angle$ D = x°

$\underline{\small \sf {\maltese \; \; \; Finding \: value \: of \: x : \; \; \; }}$

We know that,

★ Sum of angles of a quadrilateral = 360°

$\longrightarrow \sf { \angle A + \angle B + \angle C + \angle D= {360}^{\circ} }$

$\longrightarrow$ x° + 3x° + x° + 3x° = 360°

$\longrightarrow$ 4x° + 4x° = 360°

$\longrightarrow$ 8x° = 360°

$\longrightarrow$ x° = $\sf \dfrac{360^{\circ}}{8}$

$\longrightarrow$ x° = 45°

So,

$\longrightarrow \sf { \angle D = x^{\circ}}$

$\longrightarrow \underline{\boxed{ \pmb {\sf{ \angle D = 45^{\circ}} }}}$

Also,

$\longrightarrow \sf { \angle C = 3x^{\circ}}$

$\longrightarrow \sf { \angle C = 3(45)^{\circ}}$

$\longrightarrow \underline{\boxed{ \pmb {\sf{ \angle C = 135^{\circ}} }}}$

Therefore, measure of $\angle$ C is 135° and measure of $\angle$ D is 45°.

Hence, we got the answer !