Question

The larger of two supplementary angles exceeds the smaller by 18°. Find the angles.​

Answer 1

Answer:

81°,99°

Step-by-step explanation:

Supplementary angles give a sum of 180°

Let's frame the equation that is,

(Let the smaller angle be x)

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x+x+18=180° (Supplementary angles)

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2x=180-18 (Shift. 18 to RHS and add both x together to form 2x)

2x=162°

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x=162/2

x=81

second angle=81+18=99°

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Answer 2

AnSwer:

Let the two angle be x and y.

According to the question,

$\sf \: x+y = 180 - - ---(1) \\ \sf \: x = y + 18 -- - --(2)$

Substituting the value of eqn (2) in (1),

$: \implies \sf \: \: \: x+y = 180 \\ \\ : \implies \sf \: \: \:(y+18)+y = 180 \\ \\ : \implies \sf \: \: \: 2y+ 18 = 180 \\ \\ : \implies \sf \: \: \:2y = 162 \\ \\ : \implies \sf \: \: \: { \underline{ \boxed{ \sf{ \purple{y= 81}}}}}$

Similarly,

Substituting the value of y in eqn (2),

$: \implies \sf \: \: \: x=y+18 \\ \\ : \implies \sf \: \: \: x=81+18 \\ \\ : \implies \sf \: \: \: { \underline{ \boxed{ \sf{ \purple{x=99}}}}}$

The 2 angles are 81° and 99°.