Question

22. Out of two complementary angles one is 15 more than the other. Find the angles
15​

Answer 1

Answer:

Let the smaller angle equal [math]x^{\circ}[/math].

The the larger angle is [math]15^{\circ}[/math] more than

[math]x^{\circ}[/math], so it is [math]x^{\circ}+15^{\circ}[/math]. The angles are complementary, so their sum is [math]90^{\circ}[/math].

So have to solve [math]x^{\circ}+x^{\circ}+15^{\circ}=90^{\circ}[/math].

Collecting like terms, get that

[math]2x^{\circ}+15^{\circ}=90^{\circ}[/math],

[math]2x^{\circ}+15^{\circ}-15^{\circ}=90^{\circ}-15^{\circ}[/math],

[math]2x^{\circ}=75^{\circ}[/math],

[math]\frac{2x^{\circ}}{2}=\frac{75^{\circ}}{2}[/math],

[math]x^{\circ}=37\frac{1}{2}^{\circ}[/math].

So the smaller angle is [math]x=37\frac{1}{2}^{\circ}[/math].

You could eliminate the degree symbols and solve [math]x+x+15=90[/math]. Don't forget to put that symbol ([math]{\circ}[/math]) back into the answer.

Answer 2

Answer:

here is your answer

Step-by-step explanation:

let the smaller angle be x

then greater angle is x + 15

since complement angle is the sum of two angle which is equal to 90°

therefore x+(x+15) = 90°

=> 2x + 15 = 90°

=> 2x = 90° - 15°

=> x = 75°/2

=> x = 37.5°

then x ( smaller angle) = 37.5°

x+15(greater angle) = 37.5° + 15°

= 52.5°

(52.5 + 37.5 = 90) hence proved also