Question

Two complementary angles differ by 34º. Find the angles.​

Answer 1

Answer:

let

x+y = 90⁰ —1

x-y = 34⁰

using elimination method

x + y = 90⁰

x - y = 34⁰

————–

2x = 124⁰

x = 62⁰

pit value of x in eq 1

x+y = 90⁰

62⁰ + y = 90⁰

y = 90⁰-62⁰

y = 28⁰

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Answer 2

Answer -:

The complementary angles are 28° and 62°.

Step-by-step explanation -:

Let the smaller angle be x.

Then the bigger angle = x + 34 (Since they differ by 34°)

Since the angles are complementary, that is, they add up to 90°, therefore, we have -:

$x + (x + 34) = 90$

$x + x +34 = 90$

$2x + 34 = 90$

$2x = 90 - 34$

$2x = 56$

$x = \frac{56}{2}$

$x = 28.$

Since the smaller angle (x) is 28°, therefore,

The bigger angle = x + 34° = 28° + 34° = 62°.

Thus, the two complementary angles are 28° and 62°.

How to verify?

To verify the numbers, just add up and see if they are 90°. Also see if their difference is 34° or not.

The two complementary angles are 28° and 62°.

28° + 62° = 90°.

They add up to 90°. Now lets see if their difference is 34°. For that, lets just subtract these numbers.

62° - 28° = 34°.

Since they differ by 34°,

Hence verified.