Video: Finding the Relation between Two given Angles Based on Their Positions

Which of the following statements applies to the given figure? [A] ∠2 and ∠3 are vertical angles. [B] ∠2 and ∠3 are corresponding angles. [C] ∠1 and ∠4 are adjacent angles. [D] ∠2 and ∠3 are adjacent angles. [E] ∠3 and ∠4 are vertical angles.

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Video Transcript

Which of the following statements applies to the given figure? Angle two and angle three are vertical angles. Angle two and angle three are corresponding angles. Angle one and angle four are adjacent angles. Angle two and angle three are adjacent angles. Or angle three and angle four are vertical angles.

We’re given a figure which has four angles. We’re given five statements about the angles. And we have to work out which one or which ones are true. Each statement contains a word describing a different type of angle. Vertical angles, corresponding angles, adjacent angles, another one which has adjacent angles, and vertical angles. The first statement is asking us to compare angle two and angle three. Here we have angle two and angle three. And we’re asked if this pair of angles are vertical angles. Vertical angles are formed when two lines intersect.

So here we have one pair of vertical angles and another pair. So are angle two and angle three vertical angles? Well, we have two lines which intersect. So we know that angle two and angle three are vertical angles. This statement is true. Are angle two and angle three corresponding angles? Corresponding angles are equal. When two lines are crossed by another line, we can get corresponding angles. Angle two and angle three are not corresponding angles. The third statement says that angle one and angle four are adjacent angles. Adjacent angles share a side and a vertex. Angle one and angle four don’t share any sides. They’re vertical angles. So this statement doesn’t apply.

The next statement says that angle two and angle three are adjacent angles. But they don’t have any common sides. They’re vertical angles. This statement doesn’t apply either. The final statement says that angle three and angle four are vertical angles. They share a common side and a common vertex. They’re adjacent angles. So this statement doesn’t apply either. The statement which applies to the given figure is the first one. Angle two and angle three are vertical angles. None of the other statements apply.

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