Question

Please help me I don’t understand how to do this

Answer 1

Answer:

Step-by-step explanation:

Given : RS and UV are the parallel lines.

m∠STV = 108°

m∠RST = 74°

a) We have to find the measure of ∠TVU.

Since RS and UV are the parallel lines and SU is the transverse.

Therefore, m∠RST = m∠TUV [alternate angles]

m∠TUV = 74°

m∠STV + m∠UTV = 180° [Supplementary angles]

108° + m∠UTV = 180°

m∠UTV = 180° - 108°

m∠UTV = 72°

Now m∠UTV + m∠TVU + m∠TUV = 180° [Sum of the angles of a triangle = 180°]

72 + m∠TVU + 74= 180

m∠TVU + 146° = 180°

m∠TVU = 180° - 146°

m∠TVU = 34°

Therefore, measure of angle TVU is 34°

b). In the triangles RST and TUV,

∠RTS ≅ ∠UTV [Vertically opposite angles]

RS and UV are the parallel lines and line RV is the transverse.

Therefore, ∠SRT ≅ ∠UVT [Alternate angles]

RS and UV are the parallel lines and line SU is the transverse.

Therefore ∠RST ≅ ∠TUV [Alternate angles]

Since all corresponding angles of both the triangles are equal. Therefore, triangles RST and TUV will be similar.

Answer 2

The answer is 72 because yeah I’m bad at explain but a line is 180 so 180-108=72