Answer:
11. m∠ABD = 28°
Other Q. m∠1 = 61°
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°