Question

If measure of angle 3= 74 find each measure

Answer 1

Answer:

A 74

B 74

C 74

D 106

E 106

F 106

G 106

Step-by-step explanation:

Subtract from 180

Hope this helps

Answer 2

This is about understanding transverse angle theorem.

∠1 = ∠5 = 74°

∠2 =∠6 = 106°

∠3 = ∠7 = 74°

∠4 = ∠8 = 106°

• We are told that ∠3 = 74°

This ∠3 forms a straight line with ∠4 and ∠2.

• From angle theorems, we know that sum of angles on a straight line is equal to 180°.

Thus;

∠4 = ∠2 = 180° - 74°

∠4 = ∠2 = 106°

• Similarly, ∠2 forms a straight line with ∠1 and so;

∠1 = 180° - 106°

∠1 = 74°

• Now, we can see two parallel lines being cut by a transversal line and from transverse angle theorem, when two or more parallel lines are cut by a transverse line, the angles that occupy the same relative position are equal and are called corresponding angles.

• From the image, we see that;

∠1 and ∠5 occupy the same relative position

∠2 and ∠6 occupy the same relative position

∠3 and ∠7 occupy the same relative position

∠4 and ∠8 occupy the same relative position

• Thus;

∠1 = ∠5 = 74°

∠2 =∠6 = 106°

∠3 = ∠7 = 74°

∠4 = ∠8 = 106°

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