To solve the problem, we analyze the trapezoid $ABCD$, where:

• $\angle A = 79^\circ$,
• $\angle C = 155^\circ$,
• We need to find $\angle B$ and $\angle D$.

Properties of a Trapezoid:

1. The sum of all interior angles in a quadrilateral is $360^\circ$. $\angle A + \angle B + \angle C + \angle D = 360^\circ$
2. In a trapezoid, adjacent angles on the same side of the non-parallel sides (legs) are supplementary if the trapezoid is an isosceles trapezoid. If not stated, assume general properties.

Step-by-Step Solution:

1. Substitute known values $\angle A = 79^\circ$ and $\angle C = 155^\circ$ into the equation: $79^\circ + \angle B + 155^\circ + \angle D = 360^\circ$

   Combine like terms: $\angle B + \angle D = 360^\circ - 234^\circ$ $\angle B + \angle D = 126^\circ$

2. Since the problem involves opposite angles at the parallel bases of the trapezoid (e.g., $AB \parallel CD$), the angles adjacent to each base pair up as supplementary.

   • This means $\angle A + \angle D = 180^\circ$ and $\angle B + \angle C = 180^\circ$.

Calculate $\angle B$:

Using $\angle B + \angle C = 180^\circ$: $\angle B + 155^\circ = 180^\circ$ $\angle B = 180^\circ - 155^\circ$ $\angle B = 25^\circ$

Calculate $\angle D$:

Using $\angle A + \angle D = 180^\circ$: $79^\circ + \angle D = 180^\circ$ $\angle D = 180^\circ - 79^\circ$ $\angle D = 101^\circ$

Final Answer:

• $\angle B = 25^\circ$,
• $\angle D = 101^\circ$.

Let me know if you'd like further clarification or a step-by-step breakdown!

Here are 5 related questions to practice:

1. How do you calculate the sum of interior angles in any quadrilateral?
2. What defines a trapezoid versus a parallelogram?
3. How do you identify supplementary angles in trapezoids?
4. How can you prove angles are congruent in an isosceles trapezoid?
5. What are the properties of adjacent angles in parallel lines cut by a transversal?

Tip: Always use the property $\text{Sum of interior angles in a quadrilateral} = 360^\circ$.