Question

Two angles of a quadrilateral are 100 and 80°. If one of the remaining two angles is double the other, find their measures​

Answer 1

Given :

• 1st angle of Quadrilateral is 100° .
• 2nd Angle of the Quadrilateral is 80° .
• One of the remaining two angles is twice the other .

To Find :

• 3rd Angle = ?
• 4th Angle = ?

$\\ \qquad{\rule{200pt}{2pt}}$

SolutioN :

$\dag$ We know That :

$\qquad \; {\red{\bigstar \; \; {\pink{\underbrace{\underline{\purple{\sf{ Sum \; of \; Angle {\small_{(Quadrilateral)}} = 360^{ \circ } }}}}}}}}$

$\dag$ According to the Question :

$\longmapsto$ Let the 3rd Angle be y .So :

$\qquad \; {\pmb{\sf{ \angle 3 = y }}}$

$\longmapsto$ 4th Angle is twice the 3rd Angle .So :

$\qquad \; {\pmb{\sf{ \angle 4 = 2y }}}$

$\dag$ Calculating the Value of y :

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { \angle 1 + \angle 2 + \angle 3 + \angle 4 = 360^{ \circ } } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { 100^{ \circ } + 80^{ \circ } + y^{ \circ } + 2y^{ \circ} = 360^{ \circ } } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { 180^{ \circ } + y^{ \circ } + 2y^{ \circ} = 360^{ \circ } } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { 180^{ \circ } + 3y^{ \circ} = 360^{ \circ } } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { 3y^{ \circ} = 360^{ \circ } - 180^{ \circ } } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { 3y^{ \circ} = 180^{ \circ } } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { y = \dfrac{180}{3} } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { y = \cancel\dfrac{180}{3} } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; {\underline{\boxed{\pmb{\frak{ y = 60 }}}}} \; {\orange{\pmb{\bigstar}}} \\ \\ \\ \end{gathered}$

$\dag$ Calculating the Angles :

• $\sf{ \angle 3 }$ = y = 60°
• $\sf{ \angle 4 }$ = 2y = 2(60) = 120°

$\therefore \;$ The rest two Angles are 60° and 120° .

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Answer 2

Answer:

Question:-

Two angles of a quadrilateral are 100 and 80°. If one of the remaining two angles is double the other, find their measures

Given:-

The two angles of a quadrilateral are 100° and 80°

To find:-

The remaining two angles which is double than the other

$\huge\mathcal\pink{Solution:-}$

Let us assume that

angle 3=x

angle 4=2x

According to the question,

Sum of all angles in a quadrilateral=360°

On substituting the given values we get,

angle a+angle b+angle c+angle d=360°

$\mapsto \: 100° + 80° + x + 2x = 360°$

$180° + 3x = 360°$

$\mapsto \: 3x = 360° - 180°$

$\mapsto \: 3x = 180°$

$x = \frac{180°}{3}$

$x = 60°$

Calculating the angles,

angle c=x=60°

angle d=2x=2(60°) =120°

Therefore the remaining two angles are 60° and 120°