Question

the angles of a quadrilateral are in the following ratio. Find the measurements of the angles. 2: 4: 6: 8​

Answer 1

Answer:

The above image shows your answer.

Answer 2

$\Large \over\begin {gathered} {\underbrace {\boxed{ \rm {\red{Given}}}}}\end{gathered}$

• Angles of quadrilateral in ratios.

$\:$

• Angles of quadrilateral in ratios are

‌ ‌ ‌ ‌ ‌ ‌ 2 : 4 : 6 : 8.

_______________________

$\Large \over\begin {gathered} {\underbrace {\boxed{ \rm {\red{To \: \: Find}}}}}\end{gathered}$

Measurements of the angles.

_______________________

$\Large \over\begin {gathered} {\underbrace {\boxed{ \rm {\red{Solution}}}}}\end{gathered}$

Let each angle of the quadrilateral be 2x , 4x , 6x and 8x.

$\:$

Sum of all the angles of a quadrilateral = 360°.

$\bf \large \: \therefore \: \: 2x \: + \: 4x \: + \: 6x \: + \: 8x \: = \: 360 \degree$

$\bf \large \: \therefore \: \:20x \: = \: 360 \degree$

$\bf \large \: \therefore \: \: \:x \: = \: \cancel\frac{360}{20} \: = \: 18 \degree$

$\bf \large \: \therefore \: \: \: x \: = \: 18 \degree$

_______________________

$\bf \large \: \rightarrow \: \:2x \: = \: 2 \: \times \: 18 \: = \: 36 \degree$

$\bf \large \: \rightarrow \: \:4x \: = \: 4 \: \times \: 18 \: = \: 72 \degree$

$\bf \large \: \rightarrow \: \:6x \: = \: 6 \: \times \: 18 \: = \: 108 \degree$

$\bf \large \: \rightarrow \: \:8x \: = \: 8 \: \times \: 18 \: = \: 144 \degree$

_______________________

☛ Required angles are :

⇨ 36° , 72° , 108° and 144°.