Question

Four angles of a pentagon are 100 degree, 175 degree and 75 degree Find the fifth angle​

Answer 1

Answer:

a Pentagon has 5 angles so....??

Answer 2

Correct Question :-

• Four angles of a pentagon are 100 degree, 175 degree, 85 degree and 75 degree. Find the fifth angle!

Given : -

• Measure of four angles of pentagon :-

$\qquad$ ⑴ First angle = 100°

$\qquad$ ⑵ Second angle = 175°

$\qquad$ ⑶ Third angle = 85°

$\qquad$ ⑷ Fourth angle = 75°

To find : -

• Fifth angle of the Pentagon=?

Solution :-

• Let the fifth angle of the Pentagon = x

Formula used :-

$\qquad$⎘ Sum of interior angles of polygon = (2n - 4) × 90°

• n = Number of sides of the polygon

$\qquad$ ☀️We need to add all the angles of the Pentagon and keep it equal to the sum of interior angles of the Pentagon.

$\qquad\small\underline{\pmb{\sf \:According \: to \: the \: question :-}}$

$\pink{\qquad\leadsto\quad \pmb {\mathfrak{100° + 175° + 85° + 75° + x = (2n - 4) × 90°}}}$

$\qquad\leadsto\quad \pmb {\mathfrak{435° + x = ((2 × 5) - 4) × 90°}}$

$\qquad\leadsto\quad \pmb {\mathfrak{435° + x = (10 - 4) × 90°}}$

$\qquad\leadsto\quad \pmb {\mathfrak{435° + x = 6 × 90°}}$

$\qquad\leadsto\quad \pmb {\mathfrak{435° + x = 540°}}$

$\qquad\leadsto\quad \pmb {\mathfrak{ x = 540° - 435°}}$

$\pink{\qquad\leadsto\quad \pmb {\mathfrak{ x = 105°}}}$

• The measure of the fifth angle of the Pentagon is = 105°

⠀⠀⠀⠀¯‎¯‎‎‎¯‎¯¯‎¯‎‎‎¯‎‎‎¯‎¯‎¯‎‎¯‎‎‎¯‎¯‎‎‎¯‎‎‎¯‎¯‎¯‎‎‎¯‎‎¯‎‎‎¯‎‎¯‎¯‎‎‎¯‎‎‎¯‎¯‎¯‎‎¯‎¯‎‎¯‎¯¯‎¯‎¯‎‎‎¯‎¯‎‎‎¯‎‎‎¯‎‎‎¯‎‎‎¯‎

⠀⠀

Verification : -

• First angle = 100°
• Second angle = 175°
• Third angle = 85°
• Fourth angle = 75°
• Fifth angle = 105°

Their sum :-

$\qquad\leadsto\quad \pmb {\mathfrak{ 100° + 175° + 85° + 75° + 105°}}$

$\qquad\leadsto\quad \pmb {\mathfrak{ 540°}}$

$\pink{\qquad\leadsto\quad \pmb {\mathfrak{ Sum _( Pentagon) = 540°}}}$

• Hence, verified..!!

⠀⠀⠀⠀¯‎¯‎‎‎¯‎¯¯‎¯‎‎‎¯‎‎‎¯‎¯‎¯‎‎¯‎‎‎¯‎¯‎‎‎¯‎‎‎¯‎¯‎¯‎‎‎¯‎‎¯‎‎‎¯‎‎¯‎¯‎‎‎¯‎‎‎¯‎¯‎¯‎‎¯‎¯‎‎¯‎¯¯‎¯‎¯‎‎‎¯‎¯‎‎‎¯‎‎‎¯‎‎‎¯‎‎‎¯‎

⠀