Question
In a parallelogram $ABCD$, $\angle \text{D}=135^\circ$. Determine the measures of $\angle\text{A}$ and $\angle\text{B}$.
✓
Answer
In a parallelogram $ABCD$ Adjacent angles are supplementary So,
$\angle\text{D}+\angle\text{C}=180^\circ$
$\angle\text{C}=180^\circ-135^\circ$
$\angle\text{C}=45^\circ$ In a parallelogram opposite sides are equal.
$\angle\text{A}=\angle\text{C}=45^\circ$
$\angle\text{B}=\angle\text{D}=135^\circ$
$\angle\text{D}+\angle\text{C}=180^\circ$
$\angle\text{C}=180^\circ-135^\circ$
$\angle\text{C}=45^\circ$ In a parallelogram opposite sides are equal.
$\angle\text{A}=\angle\text{C}=45^\circ$
$\angle\text{B}=\angle\text{D}=135^\circ$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Factorise: $\text{x}^2+\frac{1}{\text{x}^2}-3$
→$ABCD$ is a parallelogram in which $\angle\text{A}=70^\circ$ Compute $\angle\text{B},\angle\text{C}$ and $\angle\text{D}$.
→If the diagonals of a quadrilateral bisect each other, then it is a parallelogram.
Various modes of tansport used by $1850$ students of a school are given below:
Draw a bar graph to represent the above data.
→|
School bus
|
Private
|
Bicycle
|
Rickshaw
|
By foot
|
|
$640$
|
$360$
|
$490$
|
$210$
|
$150$
|
A cylinder, a cone and a sphere are of the same radius and same height. Find the ratio of their curved surface.
The area of a trapezium is $475\ cm^2$ and the height is $19\ cm$. Find the lengths of its two parallel sides if one side is $4\ cm$ greater than the other.
→In the given figure, $\text{ABCD}$ is a cyclic quadrilateral whose diagonals intersect at $P$ such that $\angle\text{DBC}=60^\circ$ and $\angle\text{BAC}=40^\circ.$ Find
$i. \angle\text{BCD}$
$ii. \angle\text{CAD}$
→$i. \angle\text{BCD}$
$ii. \angle\text{CAD}$
Represent geometrically the following numbers on the number line:
$\sqrt{5.6}$
→$\sqrt{5.6}$
Sides of a triangle are in the ratio of $12: 17: 25$ and its perimeter is $540 \ cm$. Find its area.
→The curved surface area of a cone is $4070cm^2$ and diameter is $70\ cm$ .What is its slant height?
→