Question

write a two - column proof for the following. given: m∠2 = 30, m∠1 = 2m∠2. prove: m∠3 + m∠4 = 90. (do not include the degree symbol in your answers.) statements: 1) m∠2 = 30 2) m∠1 = 2m∠2 3) m∠1 = 2( ) reasons: 1) given 2) given 3) substitution

Explanation:

Step1: Find the measure of ∠1

Given m∠2 = 30 and m∠1 = 2m∠2, so m∠1=2×30 = 60.

Step2: Use angle - sum property

Since the sum of angles around a point is 360 and the angles in the figure are related such that m∠3 + m∠4+m∠1 + m∠2=180 (assuming a linear - pair or relevant angle - relationship in the un - named figure). Substituting the known values of m∠1 = 60 and m∠2 = 30, we get m∠3 + m∠4+60 + 30=180.

Step3: Solve for m∠3 + m∠4

m∠3 + m∠4=180-(60 + 30)=90.

Answer:

The two - column proof can be written as follows:

Statements	Reasons
2. m∠1 = 2m∠2	Given
3. m∠1=60	Substitution (m∠2 = 30 into m∠1 = 2m∠2)
4. m∠3 + m∠4+m∠1 + m∠2 = 180	Angle - sum property (assumed relevant angle relationship in the figure)
5. m∠3 + m∠4+60 + 30 = 180	Substitution (m∠1 = 60 and m∠2 = 30 into m∠3 + m∠4+m∠1 + m∠2 = 180)
6. m∠3 + m∠4=90	Simplification of the equation m∠3 + m∠4+60 + 30 = 180