Question

Two complementary angles differ by 14 degree. What is the larger angle.

Answer 1

Answer:

$\textsf{The larger angle is }\mathsf{52^{\circ}}$

Step-by-step explanation:

$\textsf{Let the two complementary angles be }\mathsf{\theta\;\&\;\;90^{\circ}-\theta}$

$\textsf{As per given data,}$

$\mathsf{\theta-(90^{\circ}-\theta)=14^{\circ}}$

$\implies\mathsf{\theta-90^{\circ}+\theta=14^{\circ}}$

$\implies\mathsf{2\theta-90^{\circ}=14^{\circ}}$

$\implies\mathsf{2\theta=90^{\circ}+14^{\circ}}$

$\implies\mathsf{2\theta=104^{\circ}}$

$\implies\mathsf{\theta=52^{\circ}}$

$\textsf{Other angle is }\mathsf{90^{\circ}-52^{\circ}=38^{\circ}}$

$\therefore\textsf{The larger angle is }\mathsf{52^{\circ}}$

Answer 2

two complementary angles differ by 14 degrees the larger angle is