2. Parallel lines rand s are cut by two transversals, parallel lines tand u.

Which angles are alternate interior angles with angle 3?
C 25 and 213
C 27 and 215
26 and 216
28 and 214

Option A: ∠5 and ∠13 are alternate interior angles with angle 3.

Solution:

To find which angles are alternate interior angles with angle 3:

Option A: ∠5 and ∠13

If t and u are parallels, then r is a transversal.

3 and 13 are alternate interior angles.

If r and s are parallels, then t is a transversal.

3 and 5 are alternate interior angles.

Therefore ∠5 and ∠13 are alternate interior angles with angle 3.

Hence it is true.

Option B: ∠7 and ∠15

∠7 is a corresponding angle of ∠3 on the same side of the transversal.

∠15 is a corresponding angle of ∠3 on the same side of the transversal.

So, ∠7 and ∠15 are not alternate interior angles with angle 3.

Hence it is not true.

Option C: ∠6 and ∠16

∠6 is an alternate exterior angle of ∠3.

∠16 is an alternate exterior angle of ∠3.

So, ∠6 and ∠16 are not alternate interior angles with angle 3.

Hence it is not true.

Option D: ∠8 and ∠14

∠8 is an interior angle on the same side.

∠14 is an interior angle on the same side.

So, ∠8 and ∠14 are not alternate interior angles with angle 3.

Hence it is not true.

Therefore ∠5 and ∠13 are alternate interior angles with angle 3.

Option A is the correct answer.

you can not drow on this

step-by-step explanation:

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°