The size of the angle marked r in the given triangle is 40°
From the diagram, we see that we have a triangle. To determine the size of the angle marked r, we will consider the exterior angle theorem.
The exterior angle theorem states that the measure of an exterior angle is equal to the sum of the measures of the two remote interior angles of the triangle.
From the diagram,
The exterior angle = 130°
One of the two remote interior angles is a right angle, that is 90°; and the other one is marked r°
∴ We can write that
r° + 90° = 130°
Solving the equation, we get
r° = 130° - 90°
r° = 40°
Hence, the size of the angle marked r is 40°
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