lines m and n are parallel. If m∠2 = 150°, find the measure of the following angles
In the diagram, lines m and n are parallel. If m∠2 = 150°, find the measure of the following angles.
∠4 = ?
A. 120º
B. 50º
C. 30º
D. 150º
Well, if lines m and n are parallel, we know that corresponding angles are congruent. That means that ∠2 is congruent to ∠4. So, if ∠2 is 150º, then ∠4 must also be 150º. So, the answer is D. 150º.
Since lines m and n are parallel, we can conclude that vertical angles are congruent.
Therefore, ∠2 and ∠4 are vertical angles and have the same measure.
Given that ∠2 = 150º, we can conclude that ∠4 = 150º.
So the answer is D. 150º.
To find the measure of ∠4, we need to use the properties of parallel lines and angles.
Since lines m and n are parallel, angles formed by a transversal crossing those lines have special relationships. One such relationship is that corresponding angles are congruent.
∠2 and ∠4 are corresponding angles. So, if we know the measure of ∠2, we can determine the measure of ∠4.
Given that m∠2 = 150º, we can conclude that ∠4 is also 150º.
Therefore, the correct answer is D. 150º.
No idea where angle 4 is, but you need to recall that
vertical angles are congruent
alternate int/exterior angles are congruent
adjacent angles are supplementary
etc.
Time to review your theorems on parallel lines and their transversals