Trying to find the measure of the numbered angle? can someone me with these! : )

As Sum of the Three Angles in a Triangle = 180°

We can write as :

Angle (1) + 40° + 90° = 180°

Angle (1) + 130° = 180°

Angle (1) = 180° - 130°

Angle (1) = 50°

As Angle (2) and 90° are Vertically opposite Angles :

Angle (2) should be Equal to 90°

Angle (2) = 90°

Angle (2) + Angle (3) + 30° = 180°

90° + Angle (3) = 30° = 180°

Angle(3) + 120° = 180°

Angle(3) = 180° - 120°

Angle(3) = 60°

As Angle (3) and Angle(4) are Vertically opposite Angles :

Angle (4) should be Equal to Angle(3)

Angle (4) = 60°

Angle(4) + Angle(5) + 60° = 180°

60° + Angle(5) + 60° = 180°

Angle(5) + 120° = 180°

Angle(5) = 180° - 120°

Angle(5) = 60°

As Angle (5) and Angle(6) are Vertically opposite Angles :

Angle (6) should be Equal to Angle(5)

Angle (6) = 60°

Angle(6) + Angle(7) + 20° = 180°

60° + Angle(7) + 20° = 180°

Angle(7) + 80° = 180°

Angle(7) = 180° - 80°

Angle(7) = 100°

a. 32 degrees

step-by-step explanation:

here we have to use the rule.

m∠e = 1/2 (major arc - minor arc)

m∠e = 1/2 (212 - 148)

m∠e = 1/2 (64)

m∠e = 32 degrees

answer: a. 32 degrees

you