The measures of the angles of the quadrilateral according the ratio
are 60°, 75°, 120° and 105°
Step-by-step explanation:
Quadrilateral is a polygon with:
1. 4 sides and 4 angles
2. The sum of the measures of its angles is 360°
The ratio of the angle measures in a quadrilateral is 4 : 5 : 8 : 7
∵ The sum of the measures of the angles of the quadrilateral = 360°
∵ The ratio of the measures of the angle is 4 : 5 : 8 : 7
∴ The sum of their ratio = 4 + 5 + 8 + 7 = 24
- Use the ratio method to find the measure of each angle
→ angle (1) : angle (2) : angle (3) : angle (4) : their sum
→ 4 : 5 : 8 : 7 : 24
→ ? : ? : ? : ? : 360°
- By using cross multiplication
∴ m∠(1) = [tex]\frac{(4)(360)}{24}[/tex]
∴ m∠(1) = 60°
∴ m∠(2) = [tex]\frac{(5)(360)}{24}[/tex]
∴ m∠(2) = 75°
∴ m∠(3) = [tex]\frac{(8)(360)}{24}[/tex]
∴ m∠(3) = 120°
∴ m∠(4) = [tex]\frac{(7)(360)}{24}[/tex]
∴ m∠(4) = 105°
The measures of the angles of the quadrilateral according the ratio
are 60°, 75°, 120° and 105°
Learn more:
You can learn more about ratio in brainly.com/question/2707032
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