Advertisements
Advertisements
प्रश्न
In the given figure, for which value of x is l1 || l2?
विकल्प
37
43
45
47
Advertisements
उत्तर
In the given problem, we need to find the value of x if l1 || l2
Here, if l1 || l2 , then using the property, “if the two lines are parallel, then the alternate interior angles are equal”, we get,
∠ABD = ∠EAB
78° = ∠EAC + ∠CAB
78° = 35° + ∠CAB
∠CAB = 78° - 35°
∠CAB = 43°
Further, applying angle sum property of the triangle
In ΔABC
∠CAB + ∠ACB + ∠CBA = 180°
43° + 90° + x = 180°
x = 180° - 133°
x = 47°
Thus, x = 47°
APPEARS IN
संबंधित प्रश्न
Find the measure of each exterior angle of an equilateral triangle.
AB is a line seg P and Q are points on opposite sides of AB such that each of them is equidistant from the points A and B (See Fig. 10.26). Show that the line PQ is perpendicular bisector of AB.
In a ΔABC, if AB = AC and ∠B = 70°, find ∠A.
The vertical angle of an isosceles triangle is 100°. Find its base angles.
Find the measure of each exterior angle of an equilateral triangle.
Two lines AB and CD intersect at O such that BC is equal and parallel to AD. Prove that the lines AB and CD bisect at O.
P is a point on the bisector of an angle ∠ABC. If the line through P parallel to AB meets BC at Q, prove that triangle BPQ is isosceles.
In a ΔPQR, if PQ = QR and L, M and N are the mid-points of the sides PQ, QR and RP
respectively. Prove that LN = MN.
Which of the following statements are true (T) and which are false (F) :
If the altitude from one vertex of a triangle bisects the opposite side, then the triangle may be isosceles.
Which of the following statements are true (T) and which are false (F):
If the bisector of the vertical angle of a triangle bisects the base, then the triangle may be isosceles.
Fill the blank in the following so that the following statement is true.
Angle opposite to equal sides of a triangle are .....
Fill the blank in the following so that the following statement is true.
If altitudes CE and BF of a triangle ABC are equal, then AB = ....
Fill the blank in the following so that the following statement is true.
In an isosceles triangle ABC with AB = AC, if BD and CE are its altitudes, then BD is …… CE.
Is it possible to draw a triangle with sides of length 2 cm, 3 cm and 7 cm?
Which of the following statements are true (T) and which are false (F)?
Sum of any two sides of a triangle is greater than twice the median drawn to the third side.
Which of the following statements are true (T) and which are false (F)?
Of all the line segments that can be drawn from a point to a line not containing it, the perpendicular line segment is the shortest one.
Fill in the blank to make the following statement true.
If two angles of a triangle are unequal, then the smaller angle has the........ side opposite to it.
If the measures of angles of a triangle are in the ratio of 3 : 4 : 5, what is the measure of the smallest angle of the triangle?
If the bisectors of the acute angles of a right triangle meet at O, then the angle at Obetween the two bisectors is
ABC is an isosceles triangle with AB = AC and D is a point on BC such that AD ⊥ BC (Figure). To prove that ∠BAD = ∠CAD, a student proceeded as follows:
In ∆ABD and ∆ACD,
AB = AC (Given)
∠B = ∠C (Because AB = AC)
and ∠ADB = ∠ADC
Therefore, ∆ABD ≅ ∆ACD (AAS)
So, ∠BAD = ∠CAD (CPCT)
What is the defect in the above arguments?
[Hint: Recall how ∠B = ∠C is proved when AB = AC].
