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\text { Three angles of a seven sided polygon are } 132^{0} \text { each and the remaining four angles are } equal. Find the value of each equal angle.

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• Transcript

Solution:

Let the measure of each equal angles are x.

Then we can write:

\begin{aligned} 3 \times 132^{0}+4 x &=(2 \times 7-4) 90^{0} \\ 4 x &=900^{0}-396 \\ 4 x &=504 \\ x &=126^{0} \end{aligned}

\text { Thus the measure of each equal angles are } 126^{\circ} \text { . }

"hello students welcome to leader homework i am tutor aaron swathi from leader learning now let us solve this question the three angles of a seven sided polygon are 132 degree each and the remaining four sides are equal find the value of each equal angle so we already know the sum of the interior angles in a polygon is n minus 2 into 80 degree first let us write that the sum of interior angles in a polygon is always equal to n minus 2 into 180 degree where n is the number of sites here we know the number of sides to be 7 therefore we could write this as 7 minus 2 into 180 degree which is equal to 5 into 180 degree now let us read the question again three angles of a seven sided polygon are one 32 degree each so in the total seven sides we know three angles to be 132 degree so we could write this as 3 into 1 32 degree plus 4 into x because these are the remaining angles so here we could take x as the angles now this is equal to the sum of the interior angles which is formed so now we could equate both the equations here on equating we get 3 into 132 degree plus 4x is equal to 5 into 180 degree we know that 3 into 132 degree will be 3 90 6 degree plus 4 x is equal to 5 into 180 degree is 900 degree therefore we get 4x is equal to 900 degree minus 396 degree therefore we get 4x is equal to 900 minus 396 is 5 0 4 degree therefore x is equal to 5 0 4 degree divided by 4 on dividing phi 0 4 by 4 we will get x is equal to 126 degree therefore we could tell the measure of the equal angles are 126 degree therefore the value of each equal angulus 126 degree if you have any doubts please post your questions in the comment box and subscribe the channel for regular updates thank you "

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