Exploring maths through problem solving

Problem of the Week

Burwood Building

There are two diagonal sets of white parallel lines marked on the side of this building in Burwood, with one set of lines perpendicular to the other set.

How many angles can you find that are the same size as the angle marked in orange?

What is the size of the angle?

Answer:

By extending the sets of parallel lines, you can see that the angles marked on this diagram are all the same size (alternate angles, corresponding angles and/or vertically opposite angles).

Angles are equal if they are vertically opposite angles, or corresponding or alternate angles in parallel lines.

There are 10 angles the same size as the orange angle.

You can see from the picture below that two of the angles plus a right angle form a revolution (360 degrees).

If the angle is Y degrees,

2 x Y + 90 = 360

2 x Y = 360 - 90

2 x Y = 270

Y = 135

Each of the marked angles is 135 degrees.

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