https://file.aiquickdraw.com/mathbot/file/1726148592824ua527ae5.jpg

The image shows a trapezium \( ABCD \) where:

- \( AD \parallel BC \)
- \( \angle A = 135^\circ \)
- \( \angle C = 42^\circ \)
- \( \angle D_2 = 118^\circ \)

The task is to calculate the size of \( \angle B_1 \).

### Approach:

1. In a trapezium, consecutive interior angles between the parallel sides are supplementary, meaning their sum is \( 180^\circ \).
   
2. For \( \angle A \) and \( \angle B_1 \), we have:
   \[
   \angle A + \angle B_1 = 180^\circ
   \]
   Substituting \( \angle A = 135^\circ \):
   \[
   135^\circ + \angle B_1 = 180^\circ
   \]
   Solving for \( \angle B_1 \):
   \[
   \angle B_1 = 180^\circ - 135^\circ = 45^\circ
   \]

Thus, the size of \( \angle B_1 \) is \( 45^\circ \).

Let me know if you'd like more details or have any other questions!

Here are 5 related questions to extend your understanding:
1. How would you calculate the sum of the interior angles of a quadrilateral?
2. What are the properties of a trapezium that make it distinct from other quadrilaterals?
3. How can we calculate the size of \( \angle D_1 \)?
4. What is the relationship between the angles \( \angle D_1 \) and \( \angle C \) in this trapezium?
5. How do the properties of parallel lines affect the angles in a trapezium?

**Tip:** When working with trapeziums, always remember that the angles between the parallel sides add up to \( 180^\circ \).

In trapezium ABCD, AD is parallel to BC, and the following angles are given: A = 135°, C = 42°, and D2 = 118°. Calculate the size of angle B1.

In this problem, we calculate angle B1 in trapezium ABCD, given that A = 135°, C = 42°, and D2 = 118°. The solution involves using the supplementary angles theorem between parallel lines. Suitable for students in Grades 7-10.

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