The diagram you've provided shows a quadrilateral with two pairs of equal sides. Since the sides opposite to the equal angles are also marked equal, this appears to be an isosceles trapezoid.

Given dataThe diagram you've provided shows a quadrilateral with two pairs of equal sides. Since the sides opposite to the equal angles are also marked equal, this appears to be an isosceles trapezoid.

Given

• One angle is $115^\circ$.
• The opposite angle is marked as $b^\circ$.

For any quadrilateral, the sum of the interior angles is always $360^\circ$.

Let me guide you step-by-step:

1. In an isosceles trapezoid, the angles on the same leg (between the unequal sides) are supplementary. That means: $115^\circ + b^\circ = 180^\circ$ Solving for $b$: $b^\circ = 180^\circ - 115^\circ = 65^\circ$

So, the value of $b^\circ$ is $65^\circ$.

Would you like further clarification on this, or more detailed steps? Here are some follow-up questions:

1. What is the sum of the interior angles of any quadrilateral?
2. How can you identify an isosceles trapezoid based on its properties?
3. Why are the angles between the unequal sides supplementary in an isosceles trapezoid?
4. If another angle was given, how would it affect the calculations for $b$?
5. Can this method be applied to other types of quadrilaterals?

Tip: Always remember, in an isosceles trapezoid, the base angles are congruent. This can help in identifying missing angles easily!