In the diagram, lines m and n are parallel. If m∠2 = 150°, find the measure of the following angles.
1.
∠4 = ?
• 120º
• 50º
• 30º
• 150º
all the angles will be either 150º or 30º
It shouldn't be hard to tell which.
To find the measure of ∠4, we need to use the properties of parallel lines and transversals.
When a transversal intersects two parallel lines, the corresponding angles are congruent.
We can see that ∠2 and ∠4 are corresponding angles, so if ∠2 measures 150°, then ∠4 will also measure 150°.
Therefore, the measure of ∠4 is 150º.
To find the measure of ∠4, you need to understand the relationship between parallel lines and angles. When a transversal (in this case, line m) intersects two parallel lines (in this case, line n), several pairs of corresponding angles are formed. One of these pairs includes ∠2 and ∠4.
Since ∠2 is given as 150° and lines m and n are parallel, we can use the fact that corresponding angles are congruent. This means that ∠4 will have the same measure as ∠2.
Therefore, the measure of ∠4 is 150°.