Answer:
the true statements are:
m∠1 = 50°
m∠2 = (x + 25)°
m∠1 + m∠2 + m∠3 = 180°
Explanation:
We can use the given information and the angle relationships in the diagram to determine which statements are true.
First, we can see that m∠1 is labeled as 50 degrees, so the statement "m∠1 = 50°" is true.
Next, we can see that m∠2 is labeled as "x + 25" degrees.
We can also see that angles ∠1, ∠2, and ∠3 form a straight line, so their sum is 180 degrees. Therefore, the statement "m∠1 + m∠2 + m∠3 = 180°" is true.
To check the statement "m∠3 = (2x + x + 25)°", we can use the fact that angles ∠2 and ∠3 are vertical angles and therefore congruent. This means that m∠2 = m∠3.
Substituting "x + 25" for m∠2 and simplifying, we get:
m∠3 = m∠2
2x + x + 25 = x + 25
3x = 0
x = 0
However, this would mean that m∠2 and m∠3 both have measures of 25 degrees, which would make m∠1 + m∠2 + m∠3 equal to 100 degrees, not 180 degrees.
Therefore, the statement "m∠3 = (2x + x + 25)°" is not true.
So, the true statements are:
m∠1 = 50°
m∠2 = (x + 25)°
m∠1 + m∠2 + m∠3 = 180°