Question

Thee angles of a quadrilateral are in the ratio of 1 : 2 : 3 : 4. What is the measure of the four angles .​

Answer 1

Step-by-step explanation:

Let the common ratio be x.

Then the measure of four angles is 1x, 2x, 3x, 4x

We know that the sum of the angles of quadrilateral is 360°.

Therefore, x + 2x + 3x + 4x = 360°

⇒ 10x = 360°

⇒ x = 360/10

⇒ x = 36

Therefore, 1x = 1 × 36 = 36°

2x = 2 × 36 = 72°

3x = 3 × 36 = 108°

4x = 4 × 36 = 144°

Hence, the measure of the four angles is 36°, 72°, 108°, and 144°

Hope it helps you

Answer 2

$\sf\large\red{\underline{\underline{Question :}}}$

• Thee angles of a quadrilateral are in the ratio of 1 : 2 : 3 : 4. What is the measure of the four angles .

$\sf\large\red{\underline{\underline{Solution :}}}$

We have angles of quadrilateral are in the ratio of 1 : 2 : 3 : 4.

So, Let the angles be 1x , 2x , 3x & 4x .

As we know ,

$\red\bigstar\underline{\underbrace{\boxed{\sf Sum \: angles\:of \: Quadrilateral = 360^{\circ}}}}$

So,

⟼ 1x + 2x + 3x + 4x = 360°

⟼ 10x = 360°

$\sf\mapsto x = \dfrac{36\cancel{0}^{\circ}}{\cancel{0}} = 36^{\circ}$

So here we have got the value of x. If we substitute it in the value that we have assumed we will get the measure of angles.

$\large\purple{\underbrace{\mathfrak{Substituting\:the\:value \:of \:\bf x :}}}$

• 1x = 1× 36° = 36°
• 2x = 2 × 36° = 72°
• 3x = 3 × 36° = 108°
• 4x = 4 × 36° = 144°

$\sf\large\red{\underline{\underline{Therefore, }}}$

• Measure of angles of Quadrilateral is 36° , 72° , 108° and 144° .