Advertisements
Advertisements
प्रश्न
ABCD is a cyclic trapezium with AD || BC. If ∠B = 70°, determine other three angles of the trapezium.
Advertisements
उत्तर
If in cyclic quadrilateral `angle B = 70°` , then we have to find the other three angles.
Since, AD is parallel to BC, So,
`angleB + angleA = 180 ` (Alternate interior angles)
`70 + angleA = 180`
`⇒ angle A = 180 - 70 = 110°`
Now, since ABCD is cyclic quadrilateral, so
`angle A + angle C = 180`
`⇒ 110 + angle C = 180`
`⇒ angle C = 180 - 110 = 70°`
And,
`angle B + angleD = 180`\
`⇒ 70 + angleD = 180`
`⇒ angleD = 180 - 70 = 110°`
APPEARS IN
संबंधित प्रश्न
Two circles intersect at two points B and C. Through B, two line segments ABD and PBQ are drawn to intersect the circles at A, D and P, Q respectively (see the given figure). Prove that ∠ACP = ∠QCD.
ABC and ADC are two right triangles with common hypotenuse AC. Prove that ∠CAD = ∠CBD.
Two congruent circles intersect each other at points A and B. Through A any line segment PAQ is drawn so that P, Q lie on the two circles. Prove that BP = BQ.
ABCD is a cyclic quadrilateral in ∠BCD = 100° and ∠ABD = 70° find ∠ADB.
If the two sides of a pair of opposite sides of a cyclic quadrilateral are equal, prove that its diagonals are equal.
Circles are described on the sides of a triangle as diameters. Prove that the circles on any two sides intersect each other on the third side (or third side produced).
Find all the angles of the given cyclic quadrilateral ABCD in the figure.
In the following figure, AOB is a diameter of the circle and C, D, E are any three points on the semi-circle. Find the value of ∠ACD + ∠BED.
If non-parallel sides of a trapezium are equal, prove that it is cyclic.
If P, Q and R are the mid-points of the sides BC, CA and AB of a triangle and AD is the perpendicular from A on BC, prove that P, Q, R and D are concyclic.
