The statements that are true regarding the angles formed by the transversal and parallel lines are:
A. m∠1 = 70°.
B. m∠2 = 110°
C. m∠6 = 70°.
E. m∠9 = 50°
H. m∠16 = 130°
How to Find the Angles Formed by a Transversal and Parallel Lines?
Given the following angle measures formed when two parallel lines ( being cut by two transversals:
- m∠4 = 70°
- m∠12 = 130°
Using relevant theorems, let's determine which of the statements are true:
Angles 4 and 1 are vertical angles, therefore they are congruent based on the vertical angles theorem.
m∠4 = m∠1
m∠1 = 70°.
m∠2 = 180 - m∠4 [linear angles theorem]
m∠2 = 180 - 70
m∠2 = 110°
m∠6 = m∠4 [base on the alternate interior angles theorem]
m∠6 = 70°.
m∠9 = 180 - m∠12 [based on the linear angles theorem]
m∠9 = 180 - 130
m∠9 = 50°
m∠16 = m∠12 [based on the corresponding angles theorem]
m∠16 = 130°
The statements that are true are:
A. m∠1 = 70°.
B. m∠2 = 110°
C. m∠6 = 70°.
E. m∠9 = 50°
H. m∠16 = 130°
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