Question

the angles of quadrilateral are in the ratio 9:11:8:12. find all the angles of the quadrilateral.​

Answer 1

Answer:

81°, 99°, 72°, 108°

Step-by-step explanation:

Ratio= 9:11:8:12

Sum of ratios= 9+11+8+12= 40

1st angle= 9/40 x 360°= 81°

2nd angle= 11/40 x 360°= 99°

3rd angle= 8/40 x 360°= 72°

4th angle= 12/40 x 360°= 108°

Therefore, the angles of the quadrilateral are 81°, 99°, 72°, and 108°

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Answer 2

$\sf \: Before \: proceeding \: with \: any \: steps \: we \: need \: to \: bring \: up \: all \: the \: numbers \\ \sf \: out \: of \: ratio \: form \: and \: multiply \: them \: with \: a \: common \: term \: lets \: say \: (x)$

$\sf \: If \: we \: multiply \: all \: the \: terms \: with \: a \: common \: (x) \: term \: we \: get : \\ \\ \sf \: \bullet 9 \times x = 9x \\ \sf \bullet \: 11 \times x = 11x \\ \sf \bullet \: 8 \times x = 8x \\ \sf \bullet \: 12 \times x = 12x$

$\sf \: Now \: if \: we \: recollect \: the \: angle \: sum \: property of \: quadrilaterals \: which \: states \colon \: \\ \\ \boxed {\sf{The \: sum \: of \: all \: the \: angles \: must \: be \: = 360 \degree}}$

$\sf \: So \: now \: we \: will \: simply \: add \: all \: the \: terms \: and \: simplify \: . \: The \: process \: is \: \colon$

$\sf \: 9x + 11x + 8x + 12x = 360 \degree \\ \sf 20x + 20x = 360 \degree \\ \sf 40 x = 360 \degree \\ \\ \sf x = \dfrac{360}{40} \\ \\ \sf \: x = \dfrac{ \cancel{360}}{ \cancel{40}} \implies \: 9$

$\sf \: Now \: as \: we \: have \: got \: the \: value \: of \: (x) \: again \: we \: will \: multiply \: it \: with \: given \\ \sf \: to \: find \: the \: value \: of \: each \: angle \colon \\ \sf \bullet \: 9 \times 9 = 81 \\ \sf \bullet 11 \times 9 = 99 \\ \sf \bullet 8 \times 9 = 72 \\ \sf \bullet 12 \times 9 = 108$

$\sf \: Thus \: the \: above \: are \: the \: values \: of \: each \: angle \: . \: \\ \sf \: For \: verification \: we \: have \: to \: add \: all \: the \: angles . \\ \\ \sf \: 81 + 99 + 72 + 108 = 360 \\ \\ \sf \: 180 + 180 = 360 \\ \\ \sf \: 360 = 360$

LHS = RHS