Questions: Given triangle ABC with AD=3x-5, find the value of 'x'.

Transcript text: Given $\triangle ABC$ with $AD=3x-5$, find the value of '$x$'.

Solution

Solution Steps

Step 1: Identify the type of triangle and given angles

The first problem involves finding the value of $ x $ in a triangle where one angle is given as 61° and the other two angles are equal (isosceles triangle).

Step 2: Use the property of the sum of angles in a triangle

In any triangle, the sum of the interior angles is always 180°. Since the triangle is isosceles, the two base angles are equal. Let the base angles be $ x $.

Step 3: Set up the equation

The sum of the angles in the triangle is: \[ x + x + 61° = 180° \]

Step 4: Solve for $ x $

Combine like terms: \[ 2x + 61° = 180° \]

Subtract 61° from both sides: \[ 2x = 119° \]

Divide by 2: \[ x = 59.5° \]