Question

Please help me understand this

Answer 1

I'll break this up into various parts.

Focus on the closed lunchbox. The vertical sides are parallel, so that means alternate interior angles 1 and 2 are congruent. Refer to the alternate interior angles theorem.

angle 1 = angle 2

angle 1 = 70 degrees, so angle 2 is also 70 degrees.

Then we can determine angle 3 by subtracting from 180

180-70 = 110 is the measure of angle 3

Answer:

angle 2 = 70 degrees

angle 3 = 110 degrees

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Now onto the part that says "Explain why angle ABC is a straight angle".

In the closed lunchbox, angles 2 and 3 combine to 180 degrees so we have a straight vertical line

A straight angle is another way of saying straight line. All straight angles have a measure of 180 degrees.

So we can say that
`\angle 2` and
`\angle \boldsymbol{3}` form a linear pair. They can be glued together to get a straight line.

When the lunchbox unfolds fully open, the angles 2 and 3 still combine to a straight line. This time the line is slanted downward.

Using notation we can write
`m \angle 2 + m\angle \boldsymbol{3} = \boldsymbol{180}^(\circ)` which is basically rephrasing what I mentioned earlier, but now it's in terms of an algebraic equation.

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Now onto the last part where angle 1 is now 60 degrees.

This means angle 2 is also 60 and angle 3 is 180-60 = 120 degrees.

This causes the open lunchbox to be more steep since angle 1 gets smaller, and angle 3 gets larger.

Side note: (angle1)+(angle3) = 180 degrees