Question

The interior angles of a pentagon are (y+13)° , (y+15)° , (y+23)° , (y+29)° and (y+40)°.
i. Find the value of y

Answer 1

Answer:

Sum of all interior angles of a pentagon is 540⁰

Step-by-step explanation:

y+13+y+15+y+23+y+29+y+40=540

5y+90=540

5y=450

y=90

Answer 2

$\huge\rm\underline\pink{GIVEN:}$

• $\large\rm{Interior\:angles\:of\:pentagon\:are\:(y+13)^{\circ},(y+15)^{\circ},(y+23)^{\circ},(y+29)^{\circ},(y+40)^{\circ}}$

$\huge\rm\underline\pink{TO\:FIND:}$

• $\large\rm{Value\:of\:y}$

$\huge\rm\underline\pink{SOLUTION:}$

$\large\rm\bold{\boxed{Sum\:of\:all\:interior\:angles\:in\:a\:pentagon\:=\:540^{\circ}}}$

$\large\rm{\implies{(y+13)^{\circ}+(y+15)^{\circ}+(y+40)^{\circ}+(y+23)^{\circ}+(y+29)^{\circ}\:=\:540^{\circ}}}$

$\large\rm{\implies{5y^{\circ}+120^{\circ}\:=\:540^{\circ}}}$

$\large\rm{\implies{5y^{\circ}\:=420^{\circ}}}$

$\large\rm{\implies{y\:=\:\frac{420}{5}\:=\:85^{\circ}}}$

$\large\rm{\therefore{The\:value\:of\:y\:is\:85^{\circ}}}$