Question

Find the value of each of the angle in y+13°,y+15°,y+23°,y+29°,y+40°.

Answer 1

Answer:

Correct Question

Find the value of each of the angle in pentagon y+13°,y+15°,y+23°,y+29°,y+40°.

Topic

Linear equation & sum of interior angle

Solution

We know that the interior angle sum of a pentagon is 540°

So All the given angle will add up to 540°

$\sf{➥(y+13)°+ (y+15)°+ (y+23)°+(y+29)°+(y+40)°= 540°}$

$\sf{➥5y + 120° = 540°} \\ \\ \sf{➥5y= 540°- 120°}$

$\sf{➥5y= 420°} \\ \\ \sf{➥y= \frac{420}{5}}$

$\sf{➥ \red{y= 84°}}$

Now subsitute the value of y in the given angles of pentagon

$\sf{➷y+13°= 84+13° = 97° }\\ \\ \sf{➷y+15°= 84+15°= 99°} \\ \\ \sf{➷y+23°= 84+23°= 107°} \\ \\\sf{➷y+29°=84+29°=113°} \\ \\ \sf{➷y+40°=84+40°=124°}$

Verification

97°+99°+107°+113°+124°= 540°

Hence verified

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