Mathematics

# In a $\triangle ABC$, it is given that $\angle A : \angle B : \angle C = 3 : 2 : 1$ and $CD \perp AC$. Find $\angle ECD$.

##### SOLUTION
In a $\triangle ABC$, it is given that
$\angle A : \angle B : \angle C = 3 : 2 : 1$

It can also be written as

$\angle A = 3x, \angle B = 2x$ and $\angle C = x$

We know that the sum of all the angles in triangle $ABC$ is $180^{\circ}$.

$\angle A + \angle B + \angle C = 180^{\circ}$

By substituting the values we get

$3x + 2x + x = 180^{\circ}$

$6x = 180^{\circ}$

By division

$x = 180/6x = 30^{\circ}$

Now by substituting the value of $x$ we get

$\angle A = 3x = 3 (30^{\circ}) = 90^{\circ}$

$\angle B = 2x = 2 (30^{\circ}) = 60^{\circ}$

$\angle C = x = 30^{\circ}$

We know that in the triangle $ABC$ exterior angle is equal to the sum of two opposite interior angles

So we can write it as

$\angle ACE = \angle A + \angle B$

By substituting the values we get

$\angle ACE = 90^{\circ} + 60^{\circ}$

$\angle ACE = 150^{\circ}$

We know that $\angle ACE$ can be written as $\angle ACD + \angle ECD$

So we can write it as

$\angle ACE = \angle ACD + \angle ECD$

By substituting the values we get

$150^{\circ} = 90^{\circ} + \angle ECD$

It is given that $CD \perp AC$ so $\angle ACD = 90^{\circ}$

On further calculation

$\angle ECD = 150^{\circ} - 90^{\circ}$

By subtraction

$\angle ECD = 60^{\circ}$

Therefore, $\angle ECD = 60^{\circ}$.

You're just one step away

Subjective Medium Published on 09th 09, 2020
Questions 120418
Subjects 10
Chapters 88
Enrolled Students 86

#### Realted Questions

Q1 Single Correct Medium
Let P be the set of all points in the plane and L be the set of all lines of the plane. Find, with proof, whether there exists a bijective function $\displaystyle f : P\rightarrow L$ such that for any three collinear points A, B, C, the lines $\displaystyle f\left ( A \right ),f\left ( B \right )$ and $\displaystyle f\left ( C \right )$ are either parallel or concurrent.
• A. There exists a  funtion.
• B. The solution has infinite functions.
• C. The solution is an  integer.
• D. No such funtions exists.

Asked in: Mathematics - Lines and Angles

1 Verified Answer | Published on 09th 09, 2020

Q2 Subjective Medium
For an angle $x^{o}$, find:
the supplementary angle

Asked in: Mathematics - Lines and Angles

1 Verified Answer | Published on 09th 09, 2020

Q3 Subjective Medium
Find the complement of the following angle:
$73^\circ$

Asked in: Mathematics - Lines and Angles

1 Verified Answer | Published on 09th 09, 2020

Q4 Subjective Medium
In figure, AB$||$CD and AB$=$DC. Which angle is equal to $\angle$CAD?

Asked in: Mathematics - Lines and Angles

1 Verified Answer | Published on 09th 09, 2020

Q5 Subjective Medium
In each of the above figure write, if any, $(i)$ each pair of vertically opposite angles, and $(ii)$ each linear pair.

Asked in: Mathematics - Lines and Angles

1 Verified Answer | Published on 09th 09, 2020