Mathematics

# In the adjoining figure, $DE$ is a chord parallel to a diameter $AC$ of the circle with centre $O$. If $\angle CBD=60^o$, calculate $\angle CDE$.

##### SOLUTION
We know that the angles in the same segment of a circle are equal

From the figure we know that $\angle CAD$ and $\angle CBD$ are in the segment $CD$

$\angle CAD =\angle CBD =60^o$

An angle in a semi-circle is a right angle

So we get

$\angle ADC =90^o$

Using the angle sum property

$\angle ACD +\angle ADC+\angle CAD =180^o$

By substituting the values

$\angle ACD +90^o +60^o =180^o$

On further calculation

$\angle ACD =180^o -90^o -60^o$

By subtraction

$ACD =180^o -150^o$

So we get

$\angle ACD =30^o$

We know that $AC || DE$ and $CD$ is a transversal

From the figure we know that $\angle ACD$ and $\angle CDE$ are alternate angles

So we get

$\angle CDE =\angle ACD =30^o$

Therefore, $\angle CDE =30^o$

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 Subjective Medium
Fill in the blanks:
If two angles are supplementary, then the sum of their measures is ______.

Asked in: Mathematics - Lines and Angles

1 Verified Answer | Published on 09th 09, 2020

Q2 Single Correct Medium
In the above figure, find the value of $x$, if the figure is a square.
• A. $40$
• B. $50$
• C. $60$
• D. $30$

Asked in: Mathematics - Lines and Angles

1 Verified Answer | Published on 09th 09, 2020

Q3 Single Correct Medium
An angle which measures more than $90^o$ but less than $180^o$ is called ___________.
• A. Acute
• B. Obtuse
• C. Right
• D. None of these

Asked in: Mathematics - Lines and Angles

1 Verified Answer | Published on 09th 09, 2020

Q4 Subjective Medium
In the given figure line AB and CD intersect at O . $\angle BOC = {36^ \circ }$. Find $\angle x$ , $\angle y$ and  $\angle z$

Asked in: Mathematics - Lines and Angles

1 Verified Answer | Published on 09th 09, 2020

Q5 Subjective Medium
If two complementary angles are in the ratio $1:5$, find them.

Asked in: Mathematics - Lines and Angles

1 Verified Answer | Published on 09th 09, 2020