State true or false:
If two lines intersect and if one pair of vertically opposite angles is formed by acute angles, then the other pair of vertically opposite angles will be formed by obtuse angles.

True

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False

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Solution

The correct option is A True
When two lines intersect, the sum of one angles from both the pairs of vertically opposite angles, is $180^{\circ}$
Now, if one pair forms an acute angles, say $θ$ be the acute angle.
Then the other angle formed be $ϕ$
hence, $θ + ϕ = 180$
$ϕ = 180 - θ$
But, $θ$ is an acute angle, hence $ϕ$ is an obtuse angle.
hence, the other pair of vertically opposite angles will be formed by obtuse angles.

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State true or false:If two lines intersect and if one pair of vertically opposite angles is formed by acute angles, then the other pair of vertically opposite angles will be formed by obtuse angles.

State true or false:
If two lines intersect and if one pair of vertically opposite angles is formed by acute angles, then the other pair of vertically opposite angles will be formed by obtuse angles.