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.
