Mathematics

# In the given figure; $AE\parallel BD$,  $AC\parallel ED$ and $AB = AC$. Find $\angle a$,

$64^o$

##### SOLUTION
$\angle EDC = 58^{\circ}$ (Vertically opposite angles)

Given $AE \parallel CD$
$c = \angle EDC = 58^{\circ}$ (Corresponding angles)

Also, $AC \parallel ED$
$\angle ACB = 58^{\circ}$ (Corresponding angles)

Since, $AB = AC$
$\angle ABC = \angle ACB$ (Isosceles triangle property)
$b = \angle ABC = 58^{\circ}$ (Corresponding angles)

Now, In $\triangle ABC$,
$\angle ABC + \angle ACB + \angle BAC = 180$
$58 + 58 + \angle BAC = 180$
$\angle BAC = 180 - 116$
$\angle BAC = 64^{\circ}$
$a = 64^{\circ}$

You're just one step away

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

#### Realted Questions

Q1 Single Correct Medium
The supplement of an acute angle is a/an __________ angle.
• A. Acute
• B. Right
• C. Straight
• D. Obtuse

Asked in: Mathematics - Lines and Angles

1 Verified Answer | Published on 09th 09, 2020

Q2 Subjective Medium
In the given figure, $AB$ and $CD$ are straight lines through the centre $O$ of a circle. If $\angle AOC=80^o$ and $\angle CDE=40^o$, find $\angle DCE$

Asked in: Mathematics - Lines and Angles

1 Verified Answer | Published on 09th 09, 2020

Q3 Single Correct Medium
In the given figure, we have $\angle 1=\angle 3$ and $\angle 2=\angle 4$, then:
• A. $\angle A=\angle D$
• B. $\angle A=\angle B$
• C. $\angle B =\angle D$
• D. $\angle A=\angle C$

Asked in: Mathematics - Lines and Angles

1 Verified Answer | Published on 09th 09, 2020

Q4 Single Correct Medium
The lines represented by $2 x+3 y-9=0$ and $4 x+6 y-18=0$ are
• A. Intersecting lines
• B. Perpendicular lines to each other
• C. Parallel lines
• D. Coincident lines

Asked in: Mathematics - Lines and Angles

1 Verified Answer | Published on 09th 09, 2020

Q5 Subjective Medium
From the adjoining figure find $x$,  i $AOB$ is a straight line. Hence complete the following
Which is an acute angle?

Asked in: Mathematics - Lines and Angles

1 Verified Answer | Published on 09th 09, 2020