In the image, we see a triangle with points $A$, $B$, and $C$. Several angles are labeled: $\angle A = w$, $\angle B = x$, and $\angle C = z$. The question is asking us to identify the correct equation among the four options:

A. $w + z = 180$

B. $w + x = 180$

C. $x + z = 180$

D. $w + y = 180$

Solution:

Since this is a triangle, we use the property that the sum of the interior angles of a triangle is always $180^\circ$. Therefore, we have:

$w + x + z = 180^\circ$

Now, let's analyze the options:

• Option B is correct because it gives $w + x = 180^\circ$, which satisfies the sum of two angles on the straight line forming part of the diagram.

Would you like further details on this, or do you have any other questions?

Related Questions:

1. What is the sum of the angles in any polygon?
2. How can you find the value of the third angle in a triangle if two angles are known?
3. What is the exterior angle theorem for triangles?
4. How can we classify triangles based on their angles?
5. What are the properties of an isosceles triangle?

Tip:

Always remember that the sum of the interior angles in any triangle is $180^\circ$, which is a fundamental property of Euclidean geometry.