Question

Find the measure of an angle that is 26 degrees less than its complement.

Answer 1

First angle = 58°

Second angle = 32°

Given

Measure of an angle that is 26 degrees less than its complement

To Find

Two angles

Solution

Let 1st angle be , " x "

So , 2nd angle = " x - 26 "

We know that , " Sum of the complementary angles is equals to 90° "

⇒ x + x - 26 = 90

⇒ 2x =90 + 26

⇒ 2x = 116

⇒ x = 58

So ,

First angle , x = 58°

Second angle ,  x - 26 = 32°

Answer 2

ANSWER✔

$\large\underline\bold{GIVEN,}$

$\dashrightarrow Major\:of\:an\:angle\:that\:is\:26\degree \\ less\:than\:its\: complement$

$\large\underline\bold{TO\:FIND,}$

$\dashrightarrow The\:major\:two\:angles.$

$\large\underline\bold{SOLUTION,}$

$\therefore Taking\:two\:angles\:as\:x\:and\:another\:one\\ \therefore\: which\:is\:less\:than\:26\degree\: \implies\: x-26$

$\therefore some\:of\:complmentary\:angles\:is\:90\degree$

$\dashrightarrow x+(x-26)=90\degree$

$\implies 2x-26=90$

$\implies 2x=90+26$

$\implies 2x=116$

$\implies x= \dfrac{116}{2}$

$\implies x= \cancel\dfrac{116}{2}$

$\implies x= 58$

$\large{\boxed{\bf{\star\:\:x=58\degree \:\: \star }}}$

$\sf\therefore \angle 1= x= 58\degree$

$\sf\therefore \angle 2= x-26= 58-26= 32\degree$

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