Question

One angle of a quatilateral neasure 120 degree and rest three angle are of equals measure .find the degree measure of each angle.
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Answer 1

Answer:

80°

Step-by-step explanation:

WE KNOW THAT SUM OF ALL ANGLES IN A QUADRILATERAL IS 360°

LET THE UNKNOWN ANGLES BE "X"

GIVEN THAT ALL ANGLES ARE EQUAL

120°+X°+X°+X°=360°

120°+3X°=360°

3X°=360°-120°

3X°=240°

X=240/3

X=80°

THEREFORE THE OTHER THREE ANGLES MEASURES ARE 80°,80°,80°.

Answer 2

Given :

• 1st Angle of Quadrilateral is 120° .
• The rest 3 angles are equal .

To Find :

• Find the 3 angles

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SolutioN :

$\dag$ Let us Assume :

$\longmapsto$ Let the equal angles be x .So :

• ∠2 = ∠3 = ∠4 = x

$\dag$ We know That :

• Sum of Angles(Quadrilateral) = 360°

$\dag$ Calculating the Value of x :

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { ∠1 + ∠2 + ∠3 + ∠4 = 360° } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { 120° + x + x + x = 360° } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { 120° + 3x = 360° } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { 3x = 360° - 120° } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { 3x = 240 } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { x = \dfrac{240}{3} } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { x = \cancel\dfrac{240}{3} } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; {\pmb{\pink{\frak{ x = 80° }}}} \\ \\ \\ \end{gathered}$

$\therefore \;$ The three equal angles of the Quadrilateral are 80° .

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