Question

2 points
18. If (3x - 15) and (x + 5) are
complementary angles , then the
angles are
0 45 and 30
O 60 and 30
O 40 and 50
O 75 and 15​

Answer 1

$\huge\bigstar{\red{\underline{\underline{GIVEN}}}}$

$\large\longrightarrow{\sf{\green{Two\: angles\: (3x-15)\degree\:and\: (x+5)°}}}$

$\huge\bigstar{\red{\underline{\underline{To\:Find\:}}}}$

$\large\longrightarrow{The\: Angles. }$

$\huge\bigstar{\red{\underline{\underline{SOLUTION}}}}$

$\large\bold\longrightarrow{\sf{\red{We\: know\: that \:two \:angles\: are\: called\: complementary \:when\: their\: measures\: add \:to \:90°.}}}$

$\huge\bold\blue{SO\: ATQ, }$

$\large\pink\Longrightarrow\pink{(3x-15)°+(x+5)°=90°}$

$\large\pink\Longrightarrow\pink{3x-15+x+5=90°}$

$\large\pink\Longrightarrow\pink{4x-10=90°}$

$\large\pink\Longrightarrow\pink{4x=90+10}$

$\large\pink\Longrightarrow\pink{4x=100}$

$\large\pink\Longrightarrow\pink{x=\frac{100}{4}}$

$\large\pink\therefore\boxed{\sf{\pink{x=25}}}$

Therefore, the angles are:-

$\large\Longrightarrow{(3x-15)=(3×25-15)=(75-15)=60°}$

$\large\Longrightarrow{(x+5)=(25+5)=30°}$

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

As we know that two angles are called complementary when their measures add to 90°

So, by adding 60° and 30° we get 90°.

$\large\therefore{\sf{\green{\underline{\underline{THE \:ANGLES\: ARE:30°, 60°}}}}}$