Advertisements
Advertisements
Question
Two angles of a quadrilateral are of measure 65° and the other two angles are equal. What is the measure of each of these two angles?
Advertisements
Solution
\[ \text{ Let x be the measure of each angle } . \]
\[\text{ Since, the sum of all the angles of a quadrilateral is } 360 °, \text{ we have: } \]
\[65° + 65° + x° + x° = 360° \]
\[ \Rightarrow 2x° + 130°= 360° \]
\[ \Rightarrow 2x° = 230° \]
\[ \Rightarrow x° = 115°\]
\[ \therefore \text{ The measure of each angle is } 115° .\]
APPEARS IN
RELATED QUESTIONS
Complete of the following, so as to make a true statement:
A quadrilateral has .... diagonals.
In a quadrilateral ABCD, CO and DO are the bisectors of ∠C and ∠D respectively. Prove that \[∠COD = \frac{1}{2}(∠A + ∠B) .\]
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.
Use the information given in the following figure to find the value of x.
Use the following figure to find the value of x
In a parallelogram ABCD, its diagonals AC and BD intersect each other at point O.
If AC = 12 cm and BD = 9 cm ; find; lengths of OA and OD.
Observe the figure below and find out their name.
ABCDE is a pentagon in which AB is parallel to DC and ∠A : ∠E : ∠D = 1 : 2 : 3. Find angle A.
In quadrilateral WXYZ, the pairs of opposite angles are ______.
In the following figure,
∠AOE is a/an ______ angle
