Can anyone help me on this ? I always struggle with this...

a. The measure of angle 2 is 63 and the measure of angle 3 is 117

b. The measure of angle 4 would be approximately 30.66...

c. The measure of angle 2 would be 17

Step-by-step explanation:

a. Angles 1 and 2 are alternate interior angles which means they are equal to each other. That means that both angles 1 and 2 and 63 degrees. Angles 2 and 3 are supplementary angles which means they add up to 180 degrees.

180-63=117 degrees

b. Angles 1 and 4 are alternate exterior angles and are also equal to each other. You would set up an equation that looks like...

74=3x-18

Add 18 to both sides

92=3x

Divide by 3 on both sides

92/3 which is approximately 30.67

c. Angle 1 and 2 are alternate interior angles. You would set the two given equations equal to each other.

3x-9=x+25

Subtract x from both sides.

2x-9=25

Add 9 to both sides.

2x=34

Divide both sides by 2.

x=17

solution:

we have to construct

∠m nt ≅ ∠p qr

the steps to draw this construction are

step 1: use a compass to draw an arc from point q which intersects the side pq at point a and the side qr at point b.

step 2: draw a segment nt and use the same width of the compass to draw an arc from point n which intersects the segment nt at a point x.

step 3:

step 4: join points n and y using a straightedge.

step 3:

option (d).maintaining the same width of the compass as ab, draw an arc from point x such that it intersects the arc drawn from n in a point y.

to draw   congruent angles , 1. width of compasses while drawing two angles should be same i.e from point at which angle has to be drawn, 2.the distance between the two points where the compass intersects the two sides should be same while drawing any two congruent angles.