Question

what will be the measure of the fourth angle of a quadrilateral if the measures of three angles is 1100,800 and 950​

Answer 1

Appropriate Question : What will be the measure of the fourth angle if the measure of three angles are 110° , 80° and 95° .

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Given :

• $\sf{ \angle 1 }$ = 95°
• $\sf{ \angle 2 }$ = 110°
• $\sf{ \angle 3 }$ = 80°

To Find :

• $\sf{ \angle 4 }$ = ?

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SolutioN :

$\dag$ We know That :

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

$\dag$ Calculating the Fourth Angle :

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

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { {110}^{ \circ } + {80}^{ \circ } + {95}^{ \circ } + \angle 4 = {360}^{ \circ } } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { {190}^{ \circ } + {95}^{ \circ } + \angle 4 = {360}^{ \circ } } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { {285}^{ \circ } + \angle 4 = {360}^{ \circ } } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { \angle 4 = {360}^{ \circ } - {285}^{ \circ } } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; {\underline{\boxed{\pmb{\sf{ \angle 4 = {75}^{ \circ } }}}}} \; {\orange{\pmb{\bigstar}}} \\ \\ \\ \end{gathered}$

$\therefore \;$ Fourth Angle of the Quadrilateral is 75° .

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Answer 2

Given:-

• 4 angles of a quadrilateral are 110°, 80° and 95°

To Find:-

• The measure of fourth angle

Solution:-

• Let the fourth angle be x
• We know that sum of all angles of a quadrilateral is 360°

ATQ:-

↠110° + 80° + 95° + x° = 360°

↠190° + 95° + x = 360°

↠285° + x = 360°

↠x = 360 - 285

↠x = 75°

• Hence the measure of the fourth angle of the quadrilateral is 75°

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