In a parallelogram $ \mathrm{ABCD}, \angle \mathrm{A}: \angle \mathrm{B}=2: 3, $ then find angle $ \mathrm{D} $.
Given:
In a parallelogram \( \mathrm{ABCD}, \angle \mathrm{A}: \angle \mathrm{B}=2: 3 \).
To do:
We have to find angle \( \mathrm{D} \).
Solution:
We know that,
Sum of the angles in a parallelogram is $360^o$ and opposite angles are equal.
Let $\angle A=2x$ and $\angle B=3x$.
This implies,
$\angle C=\angle A=2x$ and $\angle D=\angle B=3x$.
Therefore,
$2x+3x+2x+3x=360^o$
$10x=360^o$
$x=\frac{360^o}{10}$
$x=36^o$
$\Rightarrow 3x=3(36^o)=108^o$
Therefore, the measure of $\angle D$ is $108^o$.
Related Articles
- Choose the correct answer from the given four options:If in triangles \( \mathrm{ABC} \) and \( \mathrm{DEF}, \frac{\mathrm{AB}}{\mathrm{DE}}=\frac{\mathrm{BC}}{\mathrm{FD}} \), then they will be similar, when(A) \( \angle \mathrm{B}=\angle \mathrm{E} \)(B) \( \angle \mathrm{A}=\angle \mathrm{D} \)(C) \( \angle \mathrm{B}=\angle \mathrm{D} \)(D) \( \angle \mathrm{A}=\angle \mathrm{F} \)
- \( \angle \mathrm{A} \) and \( \angle \mathrm{B} \) are supplementary angles. \( \angle \mathrm{A} \) is thrice \( \angle \mathrm{B} \). Find the measures of \( \angle \mathrm{A} \) and \( \angle \mathrm{B} \)\( \angle \mathrm{A}=\ldots \ldots, \quad \angle \mathrm{B}=\ldots \ldots \)
- \( \mathrm{ABCD} \) is a rhombus. Show that diagonal \( \mathrm{AC} \) bisects \( \angle \mathrm{A} \) as well as \( \angle \mathrm{C} \) and diagonal \( \mathrm{BD} \) bisects \( \angle \mathrm{B} \) as well as \( \angle \mathrm{D} \).
- \( \mathrm{ABCD} \) is a rectangle in which diagonal \( \mathrm{AC} \) bisects \( \angle \mathrm{A} \) as well as \( \angle \mathrm{C} \). Show that:(i) \( \mathrm{ABCD} \) is a square (ii) diagonal \( \mathrm{BD} \) bisects \( \angle \mathrm{B} \) as well as \( \angle \mathrm{D} \).
- \( \triangle \mathrm{ABC} \sim \triangle \mathrm{PQR} \). If \( 2 \angle \mathrm{P}=3 \angle \mathrm{Q} \) and \( \angle C=100^{\circ} \), find \( \angle B \).
- \( \triangle \mathrm{ABC} \sim \triangle \mathrm{QPR} . \) If \( \angle \mathrm{A}+\angle \mathrm{B}=130^{\circ} \) and \( \angle B+\angle C=125^{\circ} \), find \( \angle Q \).
- \( \mathrm{ABC} \) is a right angled triangle in which \( \angle \mathrm{A}=90^{\circ} \) and \( \mathrm{AB}=\mathrm{AC} \). Find \( \angle \mathrm{B} \) and \( \angle \mathrm{C} \).
- In a quadrilateral \( \mathrm{ABCD}, \angle \mathrm{A}+\angle \mathrm{D}=90^{\circ} \). Prove that \( \mathrm{AC}^{2}+\mathrm{BD}^{2}=\mathrm{AD}^{2}+\mathrm{BC}^{2} \) [Hint: Produce \( \mathrm{AB} \) and DC to meet at E]
- \( \mathrm{ABCD} \) is a cyclic quadrilateral whose diagonals intersect at a point \( \mathrm{E} \). If \( \angle \mathrm{DBC}=70^{\circ} \), \( \angle \mathrm{BAC} \) is \( 30^{\circ} \), find \( \angle \mathrm{BCD} \). Further, if \( \mathrm{AB}=\mathrm{BC} \), find \( \angle \mathrm{ECD} \).
- In \( \triangle \mathrm{ABC}, \angle \mathrm{A}=\angle \mathrm{B}+\angle \mathrm{C} \) and \( \mathrm{AM} \) is an altitude. If \( \mathrm{AM}=\sqrt{12} \) and \( \mathrm{BC}=8 \), find BM.
- Choose the correct answer from the given four options:It is given that \( \triangle \mathrm{ABC} \sim \triangle \mathrm{DFE}, \angle \mathrm{A}=30^{\circ}, \angle \mathrm{C}=50^{\circ}, \mathrm{AB}=5 \mathrm{~cm}, \mathrm{AC}=8 \mathrm{~cm} \) and \( D F=7.5 \mathrm{~cm} \). Then, the following is true:(A) \( \mathrm{DE}=12 \mathrm{~cm}, \angle \mathrm{F}=50^{\circ} \)(B) \( \mathrm{DE}=12 \mathrm{~cm}, \angle \mathrm{F}=100^{\circ} \)(C) \( \mathrm{EF}=12 \mathrm{~cm}, \angle \mathrm{D}=100^{\circ} \)(D) \( \mathrm{EF}=12 \mathrm{~cm}, \angle \mathrm{D}=30^{\circ} \)
- In figure below, if \( \angle \mathrm{ACB}=\angle \mathrm{CDA}, \mathrm{AC}=8 \mathrm{~cm} \) and \( \mathrm{AD}=3 \mathrm{~cm} \), find \( \mathrm{BD} \)."
Kickstart Your Career
Get certified by completing the course
Get Started
Data Structure
Networking
RDBMS
Operating System
Java
MS Excel
iOS
HTML
CSS
Android
Python
C Programming
C++
C#
MongoDB
MySQL
Javascript
PHP
Physics
Chemistry
Biology
Mathematics
English
Economics
Psychology
Social Studies
Fashion Studies
Legal Studies