Advertisements
Advertisements
प्रश्न
In a quadrilateral ABCD, ∠A = 72° and ∠C is the supplementary of ∠A. The other two angles are 2x – 10 and x + 4. Find the value of x and the measure of all the angles
उत्तर
∠A = 72°
∠C = 180° – 12° ...(∠A and ∠C are supplementary)
= 108°
∠A + ∠B + ∠C + ∠D = 360° ...(Total angles of quadrilateral)
72° + 2x – 10 + 108° + x + 4 = 360°
3x + 174° = 360°
x = `(186^circ)/3`
= 62°
The value of x is 62°
∠B = 2x – 10
= 2(62°) – 10
= 124° – 10°
= 114°
∠D = x + 4
= 62° + 4
= 66°
The other angles are 114°, 62° and 66°.
APPEARS IN
संबंधित प्रश्न
What is the sum of the measures of the angels of a convex quadrilateral? Will this property hold if the quadrilateral is not convex? (Make a non-convex quadrilateral and try!)
ABCD is a parallelogram, AD is produced to E so that DE = DC and EC produced meets AB produced in F. Prove that BF = BC.
In a quadrilateral, define of the following Diagonals .
In Fig. 16.19, ABCD is a quadrilateral.
Name a pair of opposite angles.
If the bisectors of two adjacent angles A and B of a quadrilateral ABCD intersect at a point O such that ∠C + ∠D = k ∠AOB, then find the value of k.
Angles of a quadrilateral are (4x)°, 5(x+2)°, (7x – 20)° and 6(x+3)°. Find :
(i) the value of x.
(ii) each angle of the quadrilateral.
Three angles of a quadrilateral are equal. If the fourth angle is 69°; find the measure of equal angles.
If APB and CQD are two parallel lines, then the bisectors of the angles APQ, BPQ, CQP and PQD form ______.
If a bicycle wheel has 48 spokes, then the angle between a pair of two consecutive spokes is ______.
Using the information given, name the right angles in part of figure:
AC ⊥ BD
