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3 years ago

Two lines intersect at a point. The vertical angles formed are supplementary.

Mathematics

1 answer:

Nastasia [14]3 years ago

8 0

we know that

Vertical angles are a pair of opposite and congruent angles formed by intersecting lines.

Let

x1---------> angle vertical 1

x2---------> angle vertical 2

x1=x2 ------> equation 1

in this problem

if the vertical angles formed are supplementary

that means that

x1+x2=180 ------> equation 2

substitute equation 1 in equation 2

x1+x1=180

2x1=180

x1=180/2

x1=90 degrees

therefore

the answer is

The vertical angles are right angles

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How do I work out this problem?

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First we need to find ∡PRQ. To do this we can use the fact that the sum of the interior angles of a triangle is 180°:

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$180=R+40+105$
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Now, we can use the fact that a strait line (like SRQ) is also 180°:
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