o the four augles of sa quadri lateral are ratio of 1:2:3:4. Find the measure of all angles of a quadrilateral
Answers
Answer:
The angles of the given quadrilateral are 36°, 72°, 108° and 144° respectively.
Step-by-step explanation:
We know that the sum of all angles in a quadrilateral is 360°
Ratio of angles = 1:2:3:4
Applying the variable to the ratio, we get
= 1x:2x:3x:4x [x is the variable here]
So,
1x + 2x + 3x + 4x = 360°
10x = 360°
x = 36°
So, multiplying the value of the variable to the ratio of each angle, we get
1x = 36°
2x = 72°
3x = 108°
4x = 144°
To verify,
The sum of all angles is 360°
36°+72°+108°+144° = 360°
Therefore, we get that the angles of the given quadrilateral are 36°, 72°, 108° and 144° respectively.
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Answer:
Step-by-step explanation:
Given , the angles of a quadrilateral ABCD are in the ratio 1:2:3:4
Let ∠A = 1x ∠B = 2x ∠C = 3x ∠D = 4x
In a quadrilateral ∠A+∠B+∠C+∠D = 360°
⇒ 1x + 2x + 3x + 4x = 360°
⇒ 10x = 360
⇒ x = 360 ÷ 10 = 36
So , the angles of the quadrilateral is
∠A = (1 × 36)° = 36°
∠B = (2 × 36)° = 72°
∠C = (3 × 36)° = 108°
∠D = (4 × 36)° = 144°