Question

If angles of a triangle are \((x+10)^\circ\), \((2x+5)^\circ\) and \((3x-15)^\circ\), then the value of \(x\) is

• A. \(40\)
• B. \(35\)
• C. \(30\)
• D. \(25\)

Hint:

Remember:
• Sum of interior angles of a triangle = \(180^\circ\).
• Form the equation by adding all three angles.
• Solve the resulting linear equation.

Answer 1

The Correct Option is C

Concept: The sum of the three interior angles of any triangle is always: \[ \boxed{180^\circ} \] This property is used to find the unknown value.

Step 1: Form the equation using the angle sum property.
Given angles are: \[ (x+10)^\circ,\quad (2x+5)^\circ,\quad (3x-15)^\circ \] Therefore, \[ (x+10)+(2x+5)+(3x-15)=180 \]

Step 2: Simplify the equation.
Combine like terms: \[ x+2x+3x+10+5-15=180 \] \[ 6x=180 \]

Step 3: Find the value of \(x\).
Divide both sides by \(6\): \[ x=\frac{180}{6}=30 \]

Step 4: Verify the result.
Substituting \(x=30\): \[ x+10=40^\circ \] \[ 2x+5=65^\circ \] \[ 3x-15=75^\circ \] Now, \[ 40^\circ+65^\circ+75^\circ=180^\circ \] Hence, the value is correct.

Step 5: Final conclusion.
Therefore, \[ \boxed{x=30} \]