Question

The measure of two complementary angles is (3x-5) degree and (x+15) degree. Find the angles.

Answer 1

Question :

The measure of two complementary angles is (3x-5) degree and (x+15) degree. Find the angles.

Answer :

$\sf\pink{Given:}$

• measure of one of the complimentary angles is 3x - 5

• measure of the other complementary angle is x + 15

$\sf{To\:find:}$

• The angles ?

Explanation :

Rule :

Complementary angles add up to 90°

Equation Formed :

• First angle + second angle = 90°

$\\ \longrightarrow\sf{ 3x - 5 + x + 15 = 90}$

$\\ \longrightarrow\sf{ 3x + x + 15 - 5 = 90}$

$\\ \longrightarrow\sf{ 4x + 10 = 90}$

$\\ \longrightarrow\sf{ 4x = 90 - 10}$

$\\ \longrightarrow\sf{ 4x = 80}$

$\\ \longrightarrow\sf{ x = \dfrac{80}{4}}$

$\\ \longrightarrow\sf{ x = 20}$

• first angle is 3x - 5

$\sf\\ \longrightarrow\sf{ 3\times 20 - 5}$

$\sf\\ \longrightarrow\sf{ 60 - 5}$

$\sf\\ \longrightarrow\sf{ 55}$

Therefore one angle is 55°

• other angle is x + 15

$\sf\\ \longrightarrow\sf{20 + 15}$

$\sf\\ \longrightarrow\sf{35}$

Therefore the other angle is 35°

$\sf\\ \longrightarrow\sf{20 + 15}$