Question

If the angles (13x + 30)° and (5x + 6)° are supplementary angles,
find the measures of these angles.​

Answer 1

Answer :

1st angle = 134°

2nd angle = 46°

Note :

★ Two angles are said to be complementary , if their sum is 90° .

★ Two angles are said to be supplementary , if their sum is 180° .

Solution :

Here ,

It is given that , the angles (13x + 30°) and (5x + 6°) are supplementary , thus their sum must be equal to 180° .

Thus ,

=> 13x + 30° + 5x + 6° = 180°

=> 18x + 36° = 180°

=> 18x = 180° - 36°

=> 18x = 144°

=> x = 144°/18

=> x = 8

Now ,

=> 1st angle = 13x + 30°

=> 1st angle = 13•8° + 30°

=> 1st angle = 104° + 30°

=> 1st angle = 134°

Also ,

=> 2nd angle = 5x + 6°

=> 2nd angle = 5•8° + 6°

=> 2nd angle = 40° + 6°

=> 2nd angle = 46°

Hence ,

1st angle = 134°

2nd angle = 46°

Answer 2

Answer:

⠀⠀ ⌬ First Angle = (13x + 30)°

⠀⠀ ⌬ Second Angle = (5x + 6)°

• Supplementary Angles are those who angles whose sum is equal to 180°

• According to the Question :

⇒ First Angle + Second Angle = 180

⇒ (13x + 30) + (5x + 6) = 180

⇒ 18x + 36 = 180

⇒ 18x = 180 - 36

⇒ x = (180 - 36)/18

⇒ x = 180/18 - 36/18

⇒ x = 10 - 2

⇒ x = 8

⠀⠀⠀⠀⠀───────────────

• Measurements of Angles

⇢ Second Angle = (5x + 6)

⇢ Second Angle = 5(8) + 6

⇢ Second Angle = 40 + 6

⇢ Second Angle = 46°

⇢ First Angle + Second Angle = 180

⇢ First Angle + 46 = 180

⇢ First Angle = 180 - 46

⇢ First Angle = 134°

∴ Required angles are of 134° & 46°.