Question

I'm studying for a quiz but I don't know how to do these two questions! Can someone explain them to me?

Answer 1

hope u can understand mate..if u have any queries please contact me..thx

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Answer 2

Answer:

11. m∠ABD = 28°

Other Q. m∠1 = 61°

Step-by-step explanation:

11) Extend line BE. Because of the Alternate Interior Angles Theorem, ∠ABE is congruent to ∠BEF. m∠BEF = 118°, so m∠ABD + m∠DBE = 118°. Because ∠DBE is a right angle, it equals 90°. So m∠ABD + 90° = 118°. So m∠ABD = 28.

Other Q.) Looking only at line a, line b, and the line next to angle 3 and angle 1. ∠3 is congruent to ∠1 + 74° by the Corresponding Angles Theorem. Now, we have:

m∠3 = m∠1 + 74°

So we have to find the measure of angle 3.

Angle 3 is supplementary to 45°, meaning their sum is 180°, because they're linear pairs.

180 - 45 = m∠3

              = 135°

Now, plug in the values to the previous:

m∠3 = m∠1 + 74°

135° = m∠1 + 74°

m∠1 = 135 - 74

        = 61°