Question

The angles of a pentagon are in the ratio 3: 5:6: 7: 9. Find the measure of each angle.​

Answer 1

The number of sides of a pentagon = 5

Interior angles property = (n-2)×180

= (5-2)×180

= 3×180

= 540

Ratio of angles of pentagon = 3:5:6:7:9.

= 3x + 5x + 6x + 7x + 9x = 540

= 30x = 540

= x = 540/30

=x = 18

Measure of each angles of pentagon = 3x = 3×18 = 54

= 5x = 5×18 = 90

= 6x = 6×18 =108

= 7x = 7×18 = 126

= 9x = 9×18 =162

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Answer 2

$\Huge{\textbf{\textsf{{\color{navy}{AN}}{\purple{SW}}{\pink{ER࿐}}{\color{pink}{:}}}}}$

$the \: number \: of \: sides \: of \: \\ a \: pentagon \: = 5$

$\red{interior \: angle \: property}$

$(n - 2) \times 180$

$=> (5 - 2 )\times 180 \\ => 3 \times 180 \\ => 540$

$to \: find \: the \: angles \: of \: \\ pentagon \: are \: in \: the \: ratio$

➡️ 3:5:6:7:9

$3 \times 5 \times 6 \times 7 \times 9 \times = 540$

$=> 30 \times = 540 \\ => x = 540 \div 30 \\ => x = 18$

$measuring \: each \: angles \: \\ of \: pentagon \: \\ 3 \times 18 = 54 \: \: \: \: \: \: \: \: \: 3x \\ 5 \times 18 = 90 \: \: \: \: \: \: \: \: \: 6x \\ 7 \times 18 = 126 \: \: \: \: \: \: \: 7x \\ 9 \times 18 = 162 \: \: \: \: \: \: \: 9x$