Advertisements
Advertisements
प्रश्न
In the given figure, if AB ⊥ BC. then x =
पर्याय
18
22
25
32
Advertisements
उत्तर
In the given figure, AB ⊥ BC
We need to find the value of x.
Now, since AB and CD are straight lines intersecting at point O, using the property, “vertically opposite angles are equal”, we get,
∠BOC = ∠AOD
∠BOC = 32°
Further, applying angle sum property of the triangle
In ΔBOC
∠BOC + ∠OBC + ∠BCO = 180°
32° + 90° + ∠BCO = 180°
∠BCO = 180° -122°
∠BCO = 58°
Then, using the property, “an exterior angle of the triangle is equal to the sum of the two opposite interior angles”, we get,
In ΔEOC
∠BCO = ∠OEC +∠EOC
58° = (x + 14)° + x
58° = 2x + 14°
2x = 58° - 14°
Further solving for x, we get,
2x = 44°
`x = (44° )/2`
x = 22°
Thus x = 22°
APPEARS IN
संबंधित प्रश्न
Show that the angles of an equilateral triangle are 60° each.
If the base of an isosceles triangle is produced on both sides, prove that the exterior angles so formed are equal to each other.
In a ΔABC, if ∠A=l20° and AB = AC. Find ∠B and ∠C.
PQR is a triangle in which PQ = PR and S is any point on the side PQ. Through S, a line is drawn parallel to QR and intersecting PR at T. Prove that PS = PT.
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°.
Which of the following statements are true (T) and which are false (F):
The measure of each angle of an equilateral triangle is 60°
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 ……
In a ΔABC, if ∠B = ∠C = 45°, which is the longest 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 angles of a triangle are unequal, then the smaller angle has the........ side opposite to it.
In a ΔABC, if ∠A = 60°, ∠B = 80° and the bisectors of ∠B and ∠C meet at O, then ∠BOC =
In the given figure, if EC || AB, ∠ECD = 70° and ∠BDO = 20°, then ∠OBD 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
M is a point on side BC of a triangle ABC such that AM is the bisector of ∠BAC. Is it true to say that perimeter of the triangle is greater than 2 AM? Give reason for your answer.
Is it possible to construct a triangle with lengths of its sides as 8 cm, 7 cm and 4 cm? Give reason for your answer.
Show that in a quadrilateral ABCD, AB + BC + CD + DA > AC + BD
