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
ABC is an isosceles triangle in which altitudes BE and CF are drawn to equal sides AC and AB respectively (see the given figure). Show that these altitudes are equal.
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 Figure AB = AC and ∠ACD =105°, find ∠BAC.
Find the measure of each exterior angle of an equilateral triangle.
In Figure 10.24, AB = AC and ∠ACD =105°, find ∠BAC.
BD and CE are bisectors of ∠B and ∠C of an isosceles ΔABC with AB = AC. Prove that BD = CE.
Which of the following statements are true (T) and which are false (F):
The two altitudes corresponding to two equal sides of a triangle need not be equal.
In ΔABC, side AB is produced to D so that BD = BC. If ∠B = 60° and ∠A = 70°, prove that: (i) AD > CD (ii) AD > AC
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)?
Difference of any two sides of a triangle is equal to 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.
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.
In the given figure, the sides BC, CA and AB of a Δ ABC have been produced to D, E and F respectively. If ∠ACD = 105° and ∠EAF = 45°, find all the angles of the Δ ABC.
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?
In the given figure, if AB ⊥ BC. then x =
In a ΔABC, ∠A = 50° and BC is produced to a point D. If the bisectors of ∠ABC and ∠ACDmeet at E, then ∠E =
Two sides of a triangle are of lengths 5 cm and 1.5 cm. The length of the third side of the triangle cannot be ______.
CDE is an equilateral triangle formed on a side CD of a square ABCD (Figure). Show that ∆ADE ≅ ∆BCE.
Find all the angles of an equilateral triangle.
