Advertisements
Advertisements
प्रश्न
In the given figure, what is the value of x?
पर्याय
35
45
50
60
Advertisements
उत्तर
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
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 and DBC are two isosceles triangles on the same base BC (see the given figure). Show that ∠ABD = ∠ACD.
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.
Prove that the medians of an equilateral triangle are equal.
In a ΔABC, if ∠A=l20° and AB = AC. Find ∠B and ∠C.
If the bisector of the exterior vertical angle of a triangle be parallel to the base. Show that the triangle is isosceles.
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°.
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 ……
In ΔABC, if ∠A = 40° and ∠B = 60°. Determine the longest and shortest sides of the triangle.
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.
Write the sum of the angles of an obtuse triangle.
In ΔABC, if ∠A = 100°, AD bisects ∠A and AD ⊥ BC. Then, ∠B =
In a ΔABC, if ∠A = 60°, ∠B = 80° and the bisectors of ∠B and ∠C meet at O, then ∠BOC =
In the given figure, x + y =
In the given figure, if AB ⊥ BC. then x =
Which of the following correctly describes the given triangle?
In ∆ABC, AB = AC and ∠B = 50°. Then ∠C is equal to ______.
Show that in a quadrilateral ABCD, AB + BC + CD + DA < 2(BD + AC)
