Advertisements
Advertisements
Question
In the following figure, BA is parallel to CD. Find the angles a, b and c:
Solution
In the given figure,
ABC is a triangle and AB || DC and AC is its transversal.
∠BAC = ∠ACD (Alternate angles)
⇒ b = 65°
Again AB || DC and BCE is its transversal
∴ ∠ABC = ∠DCE
⇒ C = 70°
But ∠ACB + ∠ACD + ∠DCE = 180 (Straight line angle)
∴ a + 65° + 70° = 180°
⇒ a + 135° = 180°
⇒ a = 180° - 135° = 45°
Hence a = 45°, b = 65° and c = 70°
APPEARS IN
RELATED QUESTIONS
Construct the 45° angle, using ruler and a pair of compass only.
Construct the 15° angle, using ruler and a pair of compass only.
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 OA = 5 cm. Use set-square to construct angle AOB = 60°, such that OB = 3 cm. Join A and B; then measure the length of AB.
Draw ∠ABC = 120°. Bisect the angle using ruler and compasses. Measure each angle so obtained and check whether or not the new angles obtained on bisecting ∠ABC are equal.
In the following figure, AB is parallel to CD; find the values of angles x, y and z:
In the following figure, AB is parallel to CD; find the values of angles x, y and z:
Two straight lines are cut by a transversal so that the co-interior angles are supplementary. Are the straight lines parallel?
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.
