Advertisements
Advertisements
Question
In the following figure, AB is parallel to CD; find the values of angles x, y and z:
Solution
In the given figure,
AB || CD
and MN is its transversal
∴ ∠LMN = ∠NMD (Alternate angles)
⇒ y = 45°
and AB || CD and LM is its transversal
∴ ∠ALM = ∠CMP (Corresponding angles)
⇒ 75° = x
∴ x = 75°
and ∠ALM = ∠LMD (Alternate angles)
⇒ 75° = z + 45°
⇒ z =75° - 45° = 30°
Hence x = 75°, y = 45° and z = 30°
APPEARS IN
RELATED QUESTIONS
Construct the 90° angle, using ruler and a pair of compass only.
Construct the 30° angle, using ruler and a pair of compass only.
Draw line AB = 6 cm. Construct angle ABC = 60°. Then draw the bisector of angle ABC.
Draw a line segment PQ = 8cm. Construct the perpendicular bisector of the line segment PQ. Let the perpendicular bisector drawn meet PQ at point R. Measure the lengths of PR and QR. Is PR = QR?
Draw a line segment AB = 6.5 cm. Locate a point P that is 5 cm from A and 4.6 cm from B. Through the point P, draw a perpendicular on to the line segment AB.
Draw a line segment OP = 8cm. Use set-square to construct ∠POQ = 90°; such that OQ = 6 cm. Join P and Q; then measure the length of PQ.
In the following figure, AB is parallel to CD; find the values of angles x, y and z:
In the following figures, PQ is parallel to RS. Find the angles a, b and c:
In the case given below, find the value of x so that POQ is straight line
Draw a line AB = 9 cm. Mark a point P in AB such that AP=5 cm. Through P draw (using set-square) perpendicular PQ = 3 cm. Measure BQ.
