Advertisements
Advertisements
प्रश्न
In the given figure, what is the value of x?
विकल्प
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
ΔABC is an isosceles triangle in which AB = AC. Side BA is produced to D such that AD = AB (see the given figure). Show that ∠BCD is a right angle.
Prove that the medians of an equilateral triangle are equal.
In a ΔABC, if ∠A=l20° and AB = AC. Find ∠B and ∠C.
In a ΔABC, if AB = AC and ∠B = 70°, find ∠A.
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.
Sides opposite to equal angles of a triangle are ......
Fill the blank in the following so that the following statement is true.
Angle opposite to equal sides of a triangle are .....
Fill the blank in the following so that the following statement is true.
In a ΔABC if ∠A = ∠C , then AB = ......
O is any point in the interior of ΔABC. Prove that
(i) AB + AC > OB + OC
(ii) AB + BC + CA > OA + QB + OC
(iii) OA + OB + OC >` 1/2`(AB + BC + CA)
Prove that the perimeter of a triangle is greater than the sum of its altitudes.
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.
Which of the following statements are true (T) and which are false (F)?
Of all the line segments that can be drawn from a point to a line not containing it, the perpendicular line segment is the shortest one.
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.
In ΔABC, if ∠A = 100°, AD bisects ∠A and AD ⊥ BC. Then, ∠B =
In the given figure, if AB ⊥ BC. then x =
In the given figure, if l1 || l2, the value of x is
In triangles ABC and PQR, AB = AC, ∠C = ∠P and ∠B = ∠Q. The two triangles are ______.
If ∆PQR ≅ ∆EDF, then is it true to say that PR = EF? Give reason for your answer
Show that in a quadrilateral ABCD, AB + BC + CD + DA < 2(BD + AC)
