Question

Two complementary angles are given by 2x and 2x-20⁰. The angles are :-


45⁰,45⁰

60⁰,40⁰

55⁰,35⁰

75⁰,55⁰


answer plzzzz​

Answer 1

$\large{\sf{\pink{\underline{\underline{☆\:GIVEN\:☆}}}}}$

$\large{\sf{Two\: complementary \:angles:-\:2x\: and\: 2x-20\degree}}$

$\large{\sf{\pink{\underline{\underline{☆\:To\:Find\:☆}}}}}$

$\large{\sf{Two\: complementary \:angles.}}$

$\large{\sf{\pink{\underline{\underline{☆\:SOLUTION \:☆}}}}}$

We know that two angles are called complementary when their measures add to 90 degrees.

$\large\blue{\bf{So\: According\:to\:the\:question,}}$

$\large\Longrightarrow{\sf{2x+(2x-20)=90\degree}}$

$\large\Longrightarrow{\sf{2x+2x-20=90\degree}}$

$\large\Longrightarrow{\sf{4x-20=90\degree}}$

$\large\Longrightarrow{\sf{4x=90+20}}$

$\large\Longrightarrow{\sf{x=\frac{110}{4}}}$

$\large\therefore\boxed{\sf{x=27.5}}$

So, the angles are:-

$\large{\sf{2x=2×27.5=55\degree}}$

$\large{\sf{2x-20=(2×27.5)-20=55-20=35\degree}}$

$\large{\sf{\pink{\underline{\underline{Now \:let's \: verify \: it:-}}}}}$

We know that two angles are called complementary when their measures add up to 90 degrees.

$\large{\sf{So \:by \:adding \:55\degree \: and \:35\degree\: we\: get\: 90\degree.}}$

Therefore,

$\large\boxed{\sf{\red{Two\:complementary \:angles\: are\: 55\degree \:and \:35\degree}}}$