Question

Assume m<22=35. Find the measure of all of the other angles in the figure given line L and line P are parallel.

Answer 1

Answer:

m∠1 = 145°

m∠3 = 35°

m∠4 = 145°

m∠5 = 145°

m∠6 = 35°

m∠7 = 35°

m∠8 = 145°

Step-by-step explanation:

In the picture attached,

line 'm' and line 'l' are the parallel lines and another line intersects these lines is a transverse.

m∠2 = 35°

Since ∠1 and ∠2 are supplementary angles,

m∠1 + m∠2 = 180°

m∠1 + 35° = 180°

m∠1 = 180° - 35°

m∠1 = 145°

∠1 ≅ ∠4 [Vertical angles]

m∠1 = m∠4 = 145°

∠2 ≅ ∠3 [Vertical angles]

m∠2 = m∠3 = 35°

∠3 ≅ ∠6 [Interior alternate angles]

m∠3 = m∠6 = 35°

Similarly, ∠4 ≅ ∠5 [Interior alternate angles]

m∠4 = m∠5 = 145°

∠6 ≅ ∠7 [Vertical angles]

m∠6 = m∠7 = 35°