Question

what is the value of b? b + 29° b - 26° b - 43° b = °

Explanation:

Step1: Apply exterior - angle property

The exterior - angle of a triangle is equal to the sum of the two non - adjacent interior angles. So, \(b + 29^{\circ}=(b - 26^{\circ})+(b - 43^{\circ})\).

Step2: Simplify the right - hand side

\((b - 26^{\circ})+(b - 43^{\circ})=b - 26^{\circ}+b - 43^{\circ}=2b-69^{\circ}\). So the equation becomes \(b + 29^{\circ}=2b-69^{\circ}\).

Step3: Solve for \(b\)

Subtract \(b\) from both sides: \(b - b+29^{\circ}=2b - b-69^{\circ}\), which gives \(29^{\circ}=b - 69^{\circ}\). Then add \(69^{\circ}\) to both sides: \(b=29^{\circ}+69^{\circ}\).

Answer:

\(b = 98^{\circ}\)