Question

what are the values of c and b? c+40° b+8° c-36° c-29° c = ° b = °

Explanation:

Step1: Use triangle exterior angle theorem

The exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. So, \(c + 40=(c - 36)+(c - 29)\)
Expand the right - hand side: \(c + 40=c-36 + c-29\)
Simplify the right - hand side: \(c + 40 = 2c-65\)
Subtract \(c\) from both sides: \(40=c - 65\)
Add 65 to both sides: \(c=40 + 65=105\)

Step2: Find the measure of the angle \(b + 8\)

First, find the sum of the two non - adjacent interior angles to the angle \(b + 8\). Wait, we can also use the fact that the sum of angles on a straight line is \(180^{\circ}\). The angle \(c + 40\) and the angle \(b + 8\) and the other angle? Wait, no. Let's use the triangle angle sum property. The sum of interior angles of a triangle is \(180^{\circ}\). The three interior angles are \(c-36\), \(c - 29\), and \(b + 8\). So \((c-36)+(c - 29)+(b + 8)=180\)
We know that \(c = 105\), substitute \(c\) into the equation: \((105-36)+(105 - 29)+(b + 8)=180\)
Calculate \(105-36 = 69\), \(105 - 29=76\)
So \(69+76+(b + 8)=180\)
\(145+(b + 8)=180\)
\(b+8=180 - 145=35\)
Subtract 8 from both sides: \(b=35 - 8 = 27\)

Answer:

\(c=\boxed{105}\), \(b=\boxed{27}\)