Question

find the measure of angle b * a b c 70° 40 70 110

Explanation:

Step1: Recall triangle - angle - sum property

The sum of interior angles of a triangle is 180°. Also, since the two sides are marked equal, the triangle is isosceles and angles opposite equal sides are equal. Let $\angle A=\angle B$.

Step2: Set up the equation

Let $\angle B = x$. We know that $\angle C = 70^{\circ}$ and $\angle A=\angle B=x$. Then $x + x+70^{\circ}=180^{\circ}$.

Step3: Solve the equation

Combining like - terms gives $2x+70^{\circ}=180^{\circ}$. Subtract 70° from both sides: $2x=180^{\circ}- 70^{\circ}=110^{\circ}$. Divide both sides by 2: $x = 55^{\circ}$. But there is a mistake above, we should use the fact that in an isosceles triangle with the non - equal angle given. Since the two sides are equal, the angles opposite them are equal. Let $\angle A=\angle B$. We know that $\angle C = 70^{\circ}$.
The sum of angles in a triangle is $A + B + C=180^{\circ}$. Substituting $A = B$ and $C = 70^{\circ}$, we get $2B+70^{\circ}=180^{\circ}$.
Subtract 70° from both sides: $2B=180^{\circ}-70^{\circ}=110^{\circ}$.
Divide both sides by 2: $B = 55^{\circ}$. However, if we assume the equal sides are the ones adjacent to $\angle B$, then $\angle A=\angle C = 70^{\circ}$.
Using the angle - sum property of a triangle $A + B + C=180^{\circ}$. Substitute $A = 70^{\circ}$ and $C = 70^{\circ}$: $70^{\circ}+B + 70^{\circ}=180^{\circ}$.
Combine like - terms: $B+140^{\circ}=180^{\circ}$.
Subtract 140° from both sides: $B = 40^{\circ}$.

Answer:

40