Question

Find missing angles a,b,c,d,e,f,g

Answer 1

All angles in the figure are
`\(74^\circ\)` for angles 1, 2, 3, and 4, while angles 6, 8, 7 are
`\(106^\circ\)`, and angle 5 is
`\(106^\circ\)` due to vertical and corresponding angle relationships.

In the given figure, we have been given the angle 3 as 74 degrees.

Through this, we can find out the measure of angle 4 because it is vertically opposite to 3. Thus angle 4 is also equal to 74 degrees.

Similarly, angle 1 is also equal to angle 3 because they are corresponding angles. Therefore, angle 1 is also equal to 74 degrees.

We can use the vertical angles reasoning with angle 1 and angle 2.

Through this argument, angle 2 is also equal to 74 degrees.

Now, let us calculate angle 6.

Angle 1 and angle 6 make a linear pair with each other.

angle 1 + angle 6 = 180

74 + angle 6 = 180

angle 6 = 180 - 74

angle 6 = 106 degrees

Therefore, angle 8 is also 106 degrees because these two are corresponding angles.

Angle 7 is vertically opposite with angle 8, hence it is also equal to 106 degrees.

Angle 5 is vertically opposite with angle 6, therefore, it is also equal to 106 degrees.