Two angles are supplementary. If the ratio of the measure of the smaller angle to that of the larger angle is 5:7. What is the measure of the smaller angle ?
Answers
Answer:
Smaller angle is 75°.
Step-by-step explanation:
Let,
Two supplementary angles be 5x and 7x
As we know that, sum of supplementary angles = 180°
★ According to the Question :
⇒ 5x + 7x = 180
⇒ 12x = 180
⇒ x = 180 / 12
⇒ x = 15
____________________________
★ Value of 5x :
⇒ 5 × 15
⇒ 75
____________________________
★ Value of 7x :
⇒ 7 × 15
⇒ 105
One angle = 75°
Other angle = 105°
Therefore, smaller angle is 75°.
Given :
Ratio between the measure of the smaller angle to that of the larger angle which is 5:7 .
To Find :
Measure of the smaller angle.
Solution :
Let the angles be 5x and 7x. As we know that supplementary angles measures 180°.
↬ 5x + 7x = 180°
↬ 12x = 180°
↬ x = 180/12
↬ x = 15°
Value of x is 15°.
Angles:
Smaller angle :
‣ 5x
‣ 5 X 15
‣ 75°
❖ Smaller angle measures 75°.
Larger angle :
‣ 7x
‣ 7 X 15
‣ 105°
❖ Larger angle measures 105°.
According to the question :
We need to find the value of the smaller angle.
❒ Smaller angle measures 75°.
Verification :
→ 7x + 5x = 180°
→ (7 X 15) + (5 X 15) = 180°
→ 105° + 75° = 180°
→ 180° = 180°
Hence, verified.
❒ Smaller angle measures 75°.
More Information :
✪ Supplementary angle measures 180°.
✪ Complementary angle measures 90° . For example : 65° and 25°.
✪Acute angle is which measures more than 0° and less than 90°.
✪Obtuse angle is which measures more than 90° and less than 180°.
✪ A right angle is which measures only 90°.
✪ A complete angle measures 180°.
✪ A reflex angle is which is always more than 180° (half a circle) but less than 360° (A full circle).