Answer:
1. We have been given that a∥b , and c is neither parallel to a nor b.
Let us see which of our given options are correct.
A. m∠7 can not be equal to m∠11 as line c is not parallel to line a.
B. m∠5 can not be equal to m∠12 as line c is not parallel to line b.
C. By alternate interior angles m∠4=m∠5 as ∠4 is inside line a and ∠5 is inside line b. Both angles are on the opposite sides of transversal.
D. Since we know that corresponding angles are congruent. We can see that ∠5 corresponds to ∠1, therefore, m∠1=m∠5.
Therefore, Option C and D are correct choices.
2. We have been given that AB∥CD and m∠4=85°. We are asked to find measure of ∠5.
Since we know that same side interior angles are supplementary. In our figure we can see that ∠4 and ∠5 are same side interior angles.
Therefore, measure of ∠5 will be 95 degrees.
Step-by-step explanation:
1. is m∠4=m∠5 by the alternate interior angle theorem.
2. Angles 4 & 3 are supplementary angles or linear pair and so they have to equal 180 and 180 - 85= 95 3 & 5 are corresponding angles so 95 should be your answer.
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