Question

question image o. solve for x (triangle with right angle at b, angles at a: (2x + 1)°, and another angle: (5x + 5)°)

Explanation:

Step1: Recall triangle angle sum

In a right triangle, the sum of the two non - right angles is \(90^{\circ}\). So, \((2x + 1)+(5x + 5)=90\).

Step2: Simplify the left - hand side

Combine like terms: \(2x+5x + 1+5 = 90\), which simplifies to \(7x+6 = 90\).

Step3: Solve for x

Subtract 6 from both sides: \(7x=90 - 6=84\). Then divide both sides by 7: \(x=\frac{84}{7}=12\).

Answer:

\(x = 12\)