Advertisements
Advertisements
Question
In the given figure, what is the value of x?
Options
35
45
50
60
Advertisements
Solution
In the given figure, we need to find the value of x.
Here, DBA is a straight line, so using the property, “angles forming a linear pair are supplementary”, we get,
∠CBA + ∠CBD = 180°
7y + 5y = 180°
12y = 180°
`y = (180°)/12`
y = 15°
Now, applying the value of y in ∠CBA and ∠BCA
∠BCA = 3y
= 3(15°)
= 45°
Also,
∠CBA = 5y
= 5(15°)
= 75°
Further, applying angle sum property of the triangle
In ΔABC
∠A + ∠B +∠C = 180°
x + 75° + 45° = 180°
x + 120°= 180°
x = 180° - 120°
x = 60°
Thus, x = 60°
APPEARS IN
RELATED QUESTIONS
Show that the angles of an equilateral triangle are 60° each.
In figure, AB = AC and DB = DC, find the ratio ∠ABD : ∠ACD
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.
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.
If the bisector of the exterior vertical angle of a triangle be parallel to the base. Show 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
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.
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 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.
Difference of any two sides of a triangle is........ than the third side.
In the given figure, if EC || AB, ∠ECD = 70° and ∠BDO = 20°, then ∠OBD is
In the given figure, for which value of x is l1 || l2?
In the given figure, the value of x is ______.
In a ΔABC, ∠A = 50° and BC is produced to a point D. If the bisectors of ∠ABC and ∠ACDmeet at E, then ∠E =
In triangles ABC and PQR, AB = AC, ∠C = ∠P and ∠B = ∠Q. The two triangles are ______.
Find all the angles of an equilateral triangle.
Show that in a quadrilateral ABCD, AB + BC + CD + DA < 2(BD + AC)
