Advertisements
Advertisements
Question
In the given figure, compute the value of x.
Advertisements
Solution
In the given figure,∠DCB = 45, ∠CBA = 45 and ∠BAD = 35
Here, we will produce AD to meet BC at E
Now, using angle sum property of the triangle
In ΔAEB
∠BAE +∠AEB + ∠EBA = 180°
∠AED + 35°+ 45° = 180°
∠AEB + 80° = 180°
∠AEB = 180° - 80°
∠AEB = 100°
Further, BEC is a straight line. So, using the property, “the angles forming a linear pair are supplementary”, we get,
∠AEB + ∠AEC = 180°
100 + ∠AEC = 180°
∠AEC = 180°- 100°
∠AEC = 80°
Also, using the property, “an exterior angle of a triangle is equal to the sum of its two opposite interior angles”
In ΔDEC, x is its exterior angle
Thus,
∠X = ∠DCE + ∠DEC
= 50° + 80°
= 130°
Therefore, X = 130°.
APPEARS IN
RELATED QUESTIONS
Compute the value of x in the following figure:
Is the following statement true and false :
All the angles of a triangle can be less than 60°
Is the following statement true and false :
A triangle can have two obtuse angles.
State, if the triangle is possible with the following angles :
60°, 60°, and 50°
State, if the triangle is possible with the following angles :
125°, 40°, and 15°
Find the value of the angle in the given figure:
As shown in the figure, Avinash is standing near his house. He can choose from two roads to go to school. Which way is shorter? Explain why.
The length of the three segments is given for constructing a triangle. Say whether a triangle with these sides can be drawn. Give the reason for your answer.
17 cm, 7 cm, 8 cm
In ΔABC, name the 
a) Three sides: _________, __________, __________
b) Three Angles: _________, __________, __________
c) Three Vertices: _________, __________, __________
What is common in the following figure?
 |
 |
| (i) | (ii) |
Is figure (i) that of triangle? if not, why?
