Question

Lines AB CD and EF intersect at o find the measure of angle AOC angle COF and angle BOF if AOE is 40° and angle BOD is 35°

Answer 1

Answer:

Step-by-step explanation:

Angle aoc = angle bod=35degree(v.o.a)

Angle bof = angle Ade =40 degree(v.o.a)

Angle cdf= 180 degree-(35+40)

= 180-75

=105

Aoc = 35 degree

Bof = 40 degree

Cof = 105 degree

Answer 2

Given:

Angle AOE=40° and Angle BOD=35°

To find:

The measure of angle AOC, COF, and BOF

Solution:

The measure of angle AOC=35°, COF=105°, and BOF=40°.

We can find the measures by following the given process-

We know that the lines AB, CD, EF intersect each other at O.

Since these are straight lines, the angles formed between them will be equal to the angle opposite to them.

AB and EF intersect each other and so

angle AOE=angle BOF=40° (Vertically opposite angles)

Similarly, AB and CD also intersect each other.

angle BOD=angle AOC=35° (Vertically opposite angles)

Now, EF is a straight line.

So, angle AOE+angle COF+angle AOC=180° (Linear pair)

On putting the values of angles, we get

40°+ angle COF+35°=180°

angle COF=180°-75°

=105°

Therefore, the measure of angle AOC=35°, COF=105°, and BOF=40°.