Question

………………………………………………..

Answer 1

x = 22

Explanation:

Given triangle PQR:

• ∠P = 2x−9
• ∠Q = 3x+5
• ∠R = 4x−14

To determine the value of 'x', we will use the fact that the sum of the interior angles of a triangle is 180°. We'll set up an equation based on this property using the given expressions for the angles, and then solve for 'x'.

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Given that the sum of the angles in a triangle is 180°, we can set up the equation:

`\Longrightarrow \angle P+\angle Q+\angle R=180 \textdegree\\\\\\\\\Longrightarrow (2x-9)+(3x+5)+(4x-14)=180 \textdegree`

Combining like terms:

`\Longrightarrow (2x+3x+4x)+(-9+5-14)=180 \\\\\\\\\Longrightarrow 9x-18=180`

Adding 18 to both sides:

`\Longrightarrow 9x=198`

Dividing both sides by 9:

`\Longrightarrow x = (198 )/(9) \\\\\\\\\therefore \boxed{x=22}`

Therefore, the value of 'x' is 22.