Question

One angle of a quadrilateral is 60° and the other
three angles are in the ratio 4:5: 6. Find the
angles.​

Answer 1

★ Given

One angle of a quadrilateral is 60°.

The other 3 angles are in the ratio 4:5:6.

★ To Find

The measures of these angles.

★ Solution

Let the unknown angles be 4x, 5x and 6x.

We know that according to the angle sum property of quadrilaterals, the sum of all the angles of a quadrilateral is 360°.

Forming an equation:

4x + 5x + 6x + 60° = 360°

15x + 60° = 360°

15x = 360 - 60

15x = 300

x = 300/15

x = 20

Therefore, the unknown angles are:

4x = 4 x 20 = 80°

5x = 5 x 20 = 100°

6x = 6 x 20 = 120°

★ Verification:

As we have got the measures of all the angles, we can check whether they are correct by adding them up:

60 + 80 + 100 + 120

= 140 + 220

= 360°

Hence, Verified!

Answer 2

Step-by-step explanation:

$\frak Given = \begin{cases} &\sf{The\ measure\ of\ one\ angle\ of\ quadilateral\ is\ 60°.} \\ &\sf{The\ other\ three\ angles\ are\ in\ the\ ratio\ of\ 4\ :\ 5\ :\ 6.} \end{cases}$

To find:- We have to find the measure of other three angles ?

☯️ Let the measure of three angles be 4x, 5x, and 6x. And the fourth angle is 60°.

__________________

$\frak{\underline{\underline{\dag As\ we\ know\ that:-}}}$

$\sf\pink{\underline{The\ sum\ of\ interior\ angles\ of\ a\ quadilateral\ is\ 360°.}}$

___________________

$\frak{\underline{\underline{\dag By\ substituting\ the\ values,\ we\ get:-}}}$

$\sf : \implies {4x\ +\ 5x\ +\ 6x\ +\ 60°\ =\ 360°} \\ \\ \sf : \implies {15x\ +\ 60°\ =\ 360°} \\ \\ \sf : \implies {15x\ =\ 360°\ -\ 60°} \\ \\ \sf : \implies {15x\ =\ 300°} \\ \\ \sf : \implies {x\ =\ \cancel \dfrac{300°}{15}} \\ \\ \sf : \implies {\purple{\underline{\boxed{\bf x\ =\ 20°.}}}}\bigstar$

$\sf \therefore {\underline{The\ value\ of\ x\ is\ 20°.}}$

So here:-

$\sf : \implies {First\ angle\ =\ 4x\ =\ 4\ ×\ 20°\ =\ 80°.}$

$\sf : \implies {Second\ angle\ =\ 5x\ =\ 5\ ×\ 20°\ =\ 100°.}$

$\sf : \implies {Third\ angle\ =\ 6x\ =\ 6\ ×\ 20°\ =\ 120°.}$

Hence:-

$\sf \therefore {\underline{The\ required\ angles\ are\ 60°(given),\ 80°,\ 100°,\ and\ 120°.}}$