Advertisements
Advertisements
प्रश्न
In the given figure, for which value of x is l1 || l2?
पर्याय
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
If the base of an isosceles triangle is produced on both sides, prove that the exterior angles so formed are equal to each other.
Prove that the medians of an equilateral triangle are equal.
If the base of an isosceles triangle is produced on both sides, prove that the exterior angles so formed are equal to each other.
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.
Angles A, B, C of a triangle ABC are equal to each other. Prove that ΔABC is equilateral.
ABC is a triangle in which ∠B = 2 ∠C. D is a point on BC such that AD bisects ∠BAC and AB = CD.
Prove that ∠BAC = 72°.
ABC is a right angled triangle in which ∠A = 90° and AB = AC. Find ∠B and ∠C.
ABC is a triangle and D is the mid-point of BC. The perpendiculars from D to AB and AC are equal. Prove that the triangle is isosceles.
Which of the following statements are true (T) and which are false (F):
Angles opposite to equal sides of a triangle are equal
In a ΔABC, if ∠B = ∠C = 45°, which is the longest side?
Fill in the blank to make the following statement true.
If two sides of a triangle are unequal, then the larger side has .... angle opposite to it.
Write the sum of the angles of an obtuse triangle.
In the given figure, if EC || AB, ∠ECD = 70° and ∠BDO = 20°, then ∠OBD is
In the given figure, if BP || CQ and AC = BC, then the measure of x is
If ∆PQR ≅ ∆EDF, then is it true to say that PR = EF? Give reason for your answer
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
Find all the angles of an equilateral triangle.
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].
Show that in a quadrilateral ABCD, AB + BC + CD + DA > AC + BD
