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Out of supplementary angles larger one is 18°greater than the smaller one .find both angle

Posted by Robert Ronnie 6 years, 5 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 5 months ago

Let the supplementary angles be x° and y° (x° > y°)
Now, x° + y° = 180 ........ (i)
and x° - y° = 18 ..(ii)
From eqn. (ii), y° = x° - 18 ...(iii)
Put (iii) in (i)
x° + x° - 18° = 180°
⇒ 2x° = 180° + 18°
⇒ 2x° = 198°
⇒ x° = 99°
On substituting {tex}x ^ { \circ } = 99 ^ { \circ }{/tex} in eqn. (iii),
{tex}y ^ { \circ } = 99 ^ { \circ } - 18 ^ { \circ } = 81 ^ { \circ }{/tex}

{tex}\therefore {/tex}{tex}y ^ { \circ } = 81 ^ { \circ }{/tex}
Hence, the angles are {tex}99 ^ { \circ } \text { and } 81 ^ { \circ }{/tex}

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