b This is an isosceles triangle which means it's legs are congruent. From the diagram, we have been given expressions for the leg's length and because they are congruent, we can equate these expressions.
6k+3^(∘)=3k+18^(∘)
Let's solve for k in this equation.
c From the diagram, we can make out two pairs of consecutive interior angles.
In both cases, the two sides cut by the third side are parallel. Therefore, we know by the Consecutive Interior Angles Theorem that they are supplementary.
w+(4t+13^(∘))=180^(∘)
w+(8t-23^(∘))=180^(∘)
Since both equations equal 180^(∘), we can by the Substitution Property of Equality equate the left-hand side of the equations.
