Question

The four angles of aquadrilateral are in the ratio 5:6:7:8.find the meadure of each angles of the quadrilateral

Answer 1

What is a quadrilateral?

➾ A quadrilateral is a polygon with four sides, four vertices or corners. The interior angles of the quadrilateral adds up-to 360°.

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Now, coming to your question:-

Given, four angles of quadrilateral are in the ratio 5 : 6 : 7 : 8

Let the constant be x

So, let the four angles be 5x, 6x, 7x and 8x

Sum of all angles of quadrilateral add upto 360°

According to the question,

5x + 6x + 7x + 8x = 360

➾ 26x = 360

➾ x = $\dfrac{360}{26}$

➾ x = 13.8 (approximately)

1st angle ➾ 5x

➾ 5 × 13.8

➾ 69°

2nd angle ➾ 6x

➾ 6 × 13.8

➾ 82.8°

3rd angle ➾ 7x

➾ 7 × 13.8

➾ 96.6°

4th angle ➾ 8x

➾ 8 × 13.8

➾ 110.4°

∴ The four angles of quadrilateral are 69°, 82.8°, 96.6° and 110.4° respectively.

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Hope my answer helps you ✌☺☺

Answer 2

Answer:

69.2°, 83.04°, 96.88°, 100,72°

Step-by-step explanation:

$\text{Given ratio of 4 angles = 5:6:7:8}\\\\\text{Let the four angles of the quadrilateral be 5x, 6x, 7x and 8x respectively.}\\\\\text{We know that the sum of the four interior angles of any quadrilateral is 360} ^\circ\\\\\therefore \: \: 5x + 6x + 7x + 8x = 360\\\\\implies 26x = 360\\\\\implies x = \dfrac{360}{26} = \boxed{13.84}\\\\\\\text{Thus, the four angles are}\\\\5 \times x = 5 \times 13.84 = 69.2 ^\circ\\\\6 \times x = 6 \times 13.84 = 83.04 ^\circ$

$7 \times x = 7 \times 13.84 = 96.88 ^\circ\\\\And, \: 8 \times 13.84 = 110.72 ^\circ\\\\\textbf{We can check our answer by adding the four angles.}\\\\\textbf{If their sum is 360, our answer is correct and if not, there is some mistake.}\\\\\text{Sum of 4 angles = 69.2 + 83.04 + 96.88 + 110.72 = 359.84}\\\\\text{which is approximately equal to 360.}}$

Hope it helped.