Suppose ∠2 and ∠4 are supplementary. Find the measure of ∠1.
A) 95°
B) 100°
C) 90°
D) 180°
E) 75°

Question

Suppose ∠2 and ∠4 are supplementary. Find the measure of ∠1. 
A) 95° 
B) 100° 
C) 90° 
D) 180° 
E) 75°

Quizplus · Accepted Answer

By definition, supplementary angles add up to 180 degrees. Therefore, we have:

∠2 + ∠4 = 180

We want to find the measurement of ∠1, which is opposite to ∠4. We know that the sum of angles in a triangle is 180 degrees, so:

∠1 + ∠4 + ∠3 = 180

∠1 + ∠4 = 180 - ∠3

Since we are given that ∠2 and ∠4 are supplementary, ∠2 + ∠4 = 180, which means that ∠4 = 180 - ∠2. Substituting this in the above equation gives:

∠1 + (180 - ∠2) = 180 - ∠3

Simplifying:

∠1 = ∠3 - ∠2

We do not have any information about ∠2 or ∠3, but we know that the sum of all angles in a triangle is 180 degrees. Therefore:

∠1 + ∠2 + ∠3 = 180

Substituting the expression we found for ∠1:

(∠3 - ∠2) + ∠2 + ∠3 = 180

Simplifying:

2∠3 = 180

∠3 = 90

Now we can use this to find ∠1:

∠1 = ∠3 - ∠2 = 90 - ∠2

We do not know the exact value of ∠2, but we know that it is less than 90 degrees (otherwise ∠3 would be greater than 90 degrees, which it cannot be since we are dealing with a triangle). Therefore, the largest possible value of ∠1 is when ∠2 = 0 (in which case ∠4 would also be 0), giving us:

∠1 = ∠3 - ∠2 = 90 - 0 = 90

Therefore, the answer is C) 90 degrees.

Suppose ∠2 and ∠4 Are Supplementary