Advertisements
Advertisements
Question
Use the information given in the following figure to find the value of x.
Advertisements
Solution
Take A, B, C, D as the vertices of Quadrilateral and BA is produced to E (say).
Since ∠EAD = 70°
∴ ∠DAB = 180° – 70°= 110° [EAB is a straight line and AD stands on it ∠EAD+ ∠DAB = 180°]
∴ 110° + 80° + 56° + 3x – 6° = 360°
[∵ sum of interior angles of a quadrilateral = 360°]
∴ 3x = 360° – 110° – 80° – 56° + 6°
3x = 360° – 240° = 120°
∴ x = 40°
RELATED QUESTIONS
How many diagonals does following have?
A convex quadrilateral
The perimeter of a parallelogram is 22 cm . If the longer side measures 6.5 cm what is the measure of the shorter side?
In a quadrilateral, define of the following Vertices .
In a quadrilateral, define of the following Opposite angles .
Complete of the following, so as to make a true statement:
A quadrilateral is convex if, for each side, the remaining ______ lie on the same side of the line containing the side.
In Fig. 16.19, ABCD is a quadrilateral.
Name a pair of opposite angles.
Three angles of a quadrilateral are equal. Fourth angle is of measure 150°. What is the measure of equal angles.
If the sum of the two angles of a quadrilateral is 180°. What is the sum of the remaining two angles?
In a quadrilateral ABCD, CO and DO are the bisectors of ∠C and ∠D respectively. Prove that \[∠COD = \frac{1}{2}(∠A + ∠B) .\]
Mark the correct alternative in each of the following:
The opposite sides of a quadrilateral have
The consecutive sides of a quadrilateral have
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.
ABCDE is a regular pentagon. The bisector of angle A of the pentagon meets the side CD in point M. Show that ∠AMC = 90°.
Write, giving reason, the name of the figure drawn alongside. Under what condition will this figure be a square.
One angle of a pentagon is 160° and the rest are all equal angles. Find the measure of the equal angles.
If one angle of a cyclic quadrilateral is 75°, then the opposite angle is
D and E are the mid-points of the sides AB and AC respectively of ∆ABC. DE is produced to F. To prove that CF is equal and parallel to DA, we need an additional information which is ______.
What is the maximum number of obtuse angles that a quadrilateral can have?
Using the information given, name the right angles in part of figure:
RS ⊥ RW
In quadrilateral PQRS, which pair represents adjacent sides?
