Question

If 2a°, 3a°,4a° and 6a° are the the angles of a quadrilateral, find them
Please show full process

Answer 1

Answer:

Given:-

Angles of a Quadiratral are=2a,3a,4a,6a

To find:-

Measures of each angle

Solution

As we know that in a Quadiratral

${\boxed{\sf Sum\:of\:angles=360°}}$

• Substitute the values

$\qquad\quad {:}\longmapsto\sf 2a+3a+4a+6a=360$

• Simplify

$\qquad\quad {:}\longmapsto\sf 5a+10a=360$

$\qquad\quad {:}\longmapsto\sf 15a=360$

$\qquad\quad {:}\longmapsto\sf a=\cancel{{\dfrac {360}{15}}}$

$\qquad\quad {:}\longmapsto\sf a=24$

__________________________

$\qquad\quad {:}\longmapsto\sf 2a=2×24=48°$

$\qquad\quad {:}\longmapsto\sf 3a=3×24=72°$

$\qquad\quad {:}\longmapsto\sf 4a=4×24=96°$

$\qquad\quad {:}\longmapsto\sf 6a=6×24=144°$

$\therefore\sf The \:angles\:are\;48°,72°,96°\:and\:144°.$

Answer 2

$\begin{gathered}\sf \large \red{\underline{ Question:-}}\\\\\end{gathered}$

If 2a°, 3a°,4a° and 6a° are the the angles of a quadrilateral, find them

$\begin{gathered}\\\\\sf \large \red{\underline{Given:-}}\\\\\end{gathered}$

Angles of the quadrilateral are given = 2a°, 3a°,4a° and 6a°

$\begin{gathered}\\\\\sf \large \red{\underline{To \: Find:-}}\\\\\end{gathered}$

The angles of the triangle.

$\begin{gathered}\\\\\sf \large \red{\underline{Solution :- }}\\\\\end{gathered}$

First we need to find the value of a to find the value of the angles of the quadrilateral:–

$\large\underbrace{ \sf { We \: know \: angles \: of \: a \: quadrilateral\: = 360 ^ \circ}}$

$\qquad \quad : \longrightarrow \sf{2a + 3a + 4a + 6a = 360}$

$\qquad \quad : \longrightarrow \sf{15a = 360}$

$\qquad \quad : \longrightarrow \sf{a = \dfrac{ \cancel{360}^{ \large24} }{ \cancel{15}} _ {\large{1}} }$

$\qquad \quad : \leadsto \underline{\boxed{\sf \pink{a = 24}}}$

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Now when we know the value of a let find the angles of the quadrilateral:–

$\qquad \quad \bull \sf \quad{2a = 2 \times 24 = \pink{48 ^ {\circ}}}$

$\qquad \quad \bull \sf \quad{3a = 3 \times 24 = \pink{72 ^ {\circ}}}$

$\qquad \quad \bull \sf \quad{4a = 4 \times 24 = \pink{96 ^{ \circ}} }$

$\qquad \quad \bull \sf \quad{6a = 6 \times 24 = \pink{144 ^ {\circ}}}$

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