Question

give breif explanation! the best answer will be marked! this question is from the internet to study for my school part! :))​

Answer 1

Answer:

math class 8 chapter 2 ex 2.2

Answer 2

Answer:

64°, 80°, 96° and 120°.

Step-by-step explanation:

As per the provided information in the given question, we have:

• Three angles of quadrilateral are in ratio 4 : 5 : 6.
• The sum of largest and smallest angle is 160°.

We've been asked to calculate all the four angles of the quadrilateral.

Let us suppose the angles of quadrilateral as 4x, 5x, 6x and y.

– Now, we know that the sum of interior angles of an quadrilateral equals to 360°. So,

$\twoheadrightarrow\quad\sf{4x+5x+6x+y=360}$

Performing addition in the LHS.

$\twoheadrightarrow\quad\sf{15x+y=360}$

Transposing +15x from LHS to RHS. It's sign will get change.

$\twoheadrightarrow\quad\sf{y=360-15x\quad\qquad\qquad \left\lgroup\begin{matrix} \sf{{eq} ^{n} \: (1)}\end{matrix}\right\rgroup \]}$

Now, let us consider the smallest angle as 4x and greatest angle as 6x. Now, according to the question, the sum of greatest and smallest angle is 160°. So,

$\twoheadrightarrow\quad\sf{4x+6x=160}$

Performing addition in LHS.

$\twoheadrightarrow\quad\sf{10x=160}$

Transposing 10 from LHS to RHS. It's arithmetic operator will get change.

$\twoheadrightarrow\quad\sf{x=\dfrac{160}{10}}$

Performing division in order to calculate the value of x.

$\twoheadrightarrow\quad\sf{x=16}$

Let us substitue the value of x in all the three angles.

$\twoheadrightarrow\quad\sf{{Angle}_{(1)}=4\times x}$

Equating value of x.

$\twoheadrightarrow\quad\sf{{Angle}_{(1)}=4\times 16}$

Performing multiplication in order to calculate the first angle.

$\twoheadrightarrow\quad\underline{\boxed{\pmb{\frak{{Angle}_{(1)}={64}^{\circ}}}}}$

Now,

$\twoheadrightarrow\quad\sf{{Angle}_{(2)}=5\times x}$

Equating value of x.

$\twoheadrightarrow\quad\sf{{Angle}_{(2)}=5\times 16}$

Performing multiplication in order to calculate the second angle.

$\twoheadrightarrow\quad\underline{\boxed{\pmb{\frak{{Angle}_{(2)}={80}^{\circ}}}}}$

Now,

$\twoheadrightarrow\quad\sf{{Angle}_{(3)}=6\times x}$

Equating value of x.

$\twoheadrightarrow\quad\sf{{Angle}_{(3)}=6\times 16}$

Performing multiplication in order to calculate the third angle.

$\twoheadrightarrow\quad\underline{\boxed{\pmb{\frak{{Angle}_{(3)}={96}^{\circ}}}}}$

Now,

$\twoheadrightarrow\quad\sf{{Angle}_{(4)}=y}$

From eqⁿ (1),

$\twoheadrightarrow\quad\sf{{Angle}_{(4)}=360-15x}$

Equating value of x.

$\twoheadrightarrow\quad\sf{{Angle}_{(4)}=360-15\times 16}$

Performing multiplication.

$\twoheadrightarrow\quad\sf{{Angle}_{(4)}=360-240}$

Performing subtraction in order to calculate the fourth angle.

$\twoheadrightarrow\quad\underline{\boxed{\pmb{\frak{{{Angle}_{(4)}={120}^{\circ}}}}}}$

Therefore, all four angles of quadrilateral are 64°, 80°, 96° and 120°.