Question

1. An angle is equal to 5 times its complement, then its measure is:
a. 25° b. 50° C. 75​

Answer 1

$\large\sf\underline{Given\::}$

• An angle is equal to 5 times it's complement .

‎

$\large\sf\underline{To\:find\::}$

• Measure of that angle .

‎

$\large\sf\underline{Assumption\::}$

Let the angle be :

• x

‎

$\large\sf\underline{Solution\::}$

We know that ,

$\sf\:Two\:angles\:a\:and\:b\:are\: complementary\:when\:$

$\small{\underline{\boxed{\mathrm\pink{a+b=90°}}}}$

‎

So for assumed angle x , the complement will be ( 90 - x )° .

‎

Now according to the question :

An angle = 5 times it's complement

• Expressing it into mathematical form

$\sf\:x=5 \times (90-x)$

$\sf\implies\:x=450-5x$

• Transposing 5x to the other side

$\sf\implies\:x+5x=450$

$\sf\implies\:6x=450$

$\sf\implies\:x=\frac{450}{6}$

$\sf\implies\:x=\cancel{\frac{450}{6}}=\frac{225}{3}$

${\sf{{\pink{\implies\:x\:=\:75°}}}}$

‎

As we got the value of x as 75° . Let's substitute its value in the assumed complement angle :

$\sf\to\:90-x\:=\:90-75\:=\: 15°$

‎

$\dag\:\underline{\sf Hence\:the\:value\:of\:the\: required\:angle \:=\:75°.}$

‎

!! Hope it helps !!

Answer 2

$\large\sf\underline{Given\::}$

An angle is equal to 5 times it's complement .

‎

$\large\sf\underline{To\:find\::}$

Measure of that angle .

‎

$\large\sf\underline{Assumption\::}$

Let the angle be :

x

‎

$\large\sf\underline{Solution\::}$

We know that ,

$\sf\:Two\:angles\:a\:and\:b\:are\: complementary\:when\:$

$\small{\underline{\boxed{\mathrm\pink{a+b=90°}}}}$

‎

So for assumed angle x , the complement will be ( 90 - x )° .

‎

Now according to the question :

An angle = 5 times it's complement

Expressing it into mathematical form

$\sf\:x=5 \times (90-x)$

$\sf\implies\:x=450-5x$

Transposing 5x to the other side

$\sf\implies\:x+5x=450$

$\sf\implies\:6x=450$

$\sf\implies\:x=\frac{450}{6}$

$\sf\implies\:x=\cancel{\frac{450}{6}}=\frac{225}{3}$

${\sf{{\pink{\implies\:x\:=\:75°}}}}$

‎

As we got the value of x as 75° . Let's substitute its value in the assumed complement angle :

$\sf\to\:90-x\:=\:90-75\:=\: 15°$

‎

$\dag\:\underline{\sf Hence\:the\:value\:of\:the\: required\:angle \:=\:75°.}$

‎

!! Hope it helps !!

copied :-)