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
ABC is a triangle in which altitudes BE and CF to sides AC and AB are equal (see the given figure). Show that
- ΔABE ≅ ΔACF
- AB = AC, i.e., ABC is an isosceles triangle.
In a ΔABC, if ∠A=l20° and AB = AC. Find ∠B and ∠C.
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.
If the base of an isosceles triangle is produced on both sides, prove that the exterior angles so formed are equal to each other.
In an isosceles triangle, if the vertex angle is twice the sum of the base angles, calculate the angles of the triangle.
PQR is a triangle in which PQ = PR and S is any point on the side PQ. Through S, a line is drawn parallel to QR and intersecting PR at T. Prove that PS = PT.
Which of the following statements are true (T) and which are false (F):
Sides opposite to equal angles of a triangle may be unequal
Fill the blank in the following so that the following statement is true.
In right triangles ABC and DEF, if hypotenuse AB = EF and side AC = DE, then ΔABC ≅ Δ ……
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)?
Sum of any two sides of a triangle is greater than the third side.
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.
ABC is a triangle. The bisector of the exterior angle at B and the bisector of ∠C intersect each other at D. Prove that ∠D = \[\frac{1}{2}\] ∠A.
Write the sum of the angles of an obtuse triangle.
In ΔABC, if ∠A = 100°, AD bisects ∠A and AD ⊥ BC. Then, ∠B =
In the given figure, what is z in terms of x and y?
In the given figure, if BP || CQ and AC = BC, then the measure of x is
In the given figure, AB and CD are parallel lines and transversal EF intersects them at Pand Q respectively. If ∠APR = 25°, ∠RQC = 30° and ∠CQF = 65°, then
In the following figure, D and E are points on side BC of a ∆ABC such that BD = CE and AD = AE. Show that ∆ABD ≅ ∆ACE.
Bisectors of the angles B and C of an isosceles triangle ABC with AB = AC intersect each other at O. Show that external angle adjacent to ∠ABC is equal to ∠BOC
