In the given figure, find x.
Answers
Answer
The value of x is 28.
Step-by-step explanation:
To Find :-
- The value of x
★ Solution
Given that,
ABC is a triangle.
- ∠A = (5x - 60)°
- ∠B = (2x + 40)°
- ∠C = (3x - 80)°
According the question,
- The value of x :-
We know,
Sum of all three interior angles of ∆ = 180°
Therefore,
⇒ ∠A + ∠B + ∠C = 180
⇒ (5x - 60) + (2x + 40) + (3x - 80) = 180
⇒ 5x - 60 + 2x + 40 + 3x - 80 = 180
⇒ 5x + 2x + 3x - 60 + 40 - 80 = 180
⇒ 10x - 100 = 180
⇒ 10x = 180 + 100
⇒ 10x = 280
⇒ x = 280/10
⇒ x = 28
We got, The value of x as 28.
Hence, The value of x is 28.
V E R I F I C A T I O N :-
- (5x - 60) + (2x + 40) + (3x - 80) = 180
By putting the value of x in L.H.S and simplifying :-
We got, [x = 28],
⇒ (5x - 60) + (2x + 40) + (3x - 80)
⇒ (5*28 - 60) + (2*28 + 40) + (3*28 - 80)
⇒ (140 - 60) + (56 + 40) + (84 - 80)
⇒ 78 + 96 + 4
⇒ 78 + 110
⇒ 180
Now, L.H.S = R.H.S = 180
Hence, Verified!
Given
- A triangle
- ∠A = 5x - 60°
- ∠B = 2x + 40°
- ∠C = 3x - 80°
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To Find
- Value of 'x'.
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Solution
We know that the sum of interior angles in a triangle is always 180°, so let's form an equation in order to find 'x'.
→ (5x - 60) + (2x + 40) + (3x - 80) = 180
Let's solve the equation step-by-step.
(5x - 60) + (2x + 40) + (3x - 80) = 180
Step 1: Simplify the equation.
→ (5x - 60) + (2x + 40) + (3x - 80) = 180
→ 5x - 60 + 2x + 40 + 3x - 80 = 180
Step 2: Combine Like Terms.
→ (5x + 2x + 3x) + (-60 + 40 - 80) = 180
→ 10x - 100 = 180
Step 3: Add 100 to both sides of the equation.
→ 10x - 100 + 100 = 180 + 100
→ 10x = 280
Step 4: Divide both sides of the equation by 10.
→ 10x ÷ 10 = 280 ÷ 10
→ x = 28
∴ The value of 'x' in the given figure is 28.
Let's find the value of each angle and verify.
∠A = 5x - 60
→ 5(28) - 60
→ 140 - 60
→ 80
∴ ∠A = 80°
∠B = 2x + 40
→ 2(28) + 40
→ 56 + 40
→ 96
∴ ∠B = 96°
∠C = 3x - 80
→ 3(28) - 80
→ 84 - 80
→ 4
∴ ∠C = 4°
Sum of ∠A, ∠B and ∠C → 80° + 96° + 4° = 180°
Hence, verified that the value of 'x' is 28.
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