40,567 views
9 votes
9 votes
In the diagram, what is the measure of angle 1 to the nearest degree?

33 degrees
55 degrees
75 degrees
105 degrees

In the diagram, what is the measure of angle 1 to the nearest degree? 33 degrees 55 degrees-example-1
User Elissa
by
2.8k points

2 Answers

11 votes
11 votes

Answer:75

Explanation:

User Andrew Adam
by
2.6k points
23 votes
23 votes

Answer:

75 degrees

Explanation:

From the first part of the diagram,

vertically opposite angles are equal,

hence we have

125° + (4x-5)° + 125° + (4x-5)° = 360°

(Angles about a point equals 360°)

4x – 5 + 4x – 5 + 125 + 125 = 360

8x + 250 – 10 = 360

8x = 360–250 + 10

8x = 120

x = 15°

Now we have (5x)° in the second part.

5x = 5 × 15 = 75°

1 is vertically opposite to angle 75°

hence it is equal to 75 degrees.

User Vivaan Kumar
by
3.3k points