Geometry basic question II 2023

Which of the following is definitely true for two lines in a plane?

m∠P is 30° more than the measure of its supplementary angle. Which of the following is the measure of ∠P?

In the given figure, the lines L1 and L2 are parallel to each other and the line segments PQ and PR are perpendicular to each other. Moreover, m ∠PQ = 55° and lines ST, PQ, and PR intersect at point P. Find m ∠TPR.

A line L1 cuts three parallel line segments AB, CD, and EF at points P, Q, and R respectively and another line L2 cuts them (AB, CD, and EF) at points S, and U respectively. If 3 × PQ = 2 × QR and the length of the segment ST is 4 cm, then what is the length of the segment TU?

As shown in the figure, line AC and line FG are parallel to each other and m ∠ABF = 55°. If ray BD and segment EF are parallel and m ∠DBF = 30°, the find m ∠EFG.

In the given figure, lines l and m are parallel to each other. Transversals AI and BK are also parallel to each other. If m ∠HJI = 50° and m ∠JHI = 45 then find m ∠CBD.

In the figure, DE and AE bisect ∠ADC and ∠DAB respectively. AB is parallel to CD. Find m ∠AED.

The lines AB, CD, EF and GH are parallel. It is known that AE : CG = 3 : 5 and AC : AG = 1 : 4. If the length of BD is 10 cm, what is the length (in cm) o FH?