Advertisements
Advertisements
प्रश्न
In the given figure, x + y =
विकल्प
270
230
210
190°
Advertisements
उत्तर
In the given figure, we need to find x+ y
Here, AB and CD are straight lines intersecting at point O, so using the property, “vertically opposite angles are equal”, we get,
∠BOD = ∠AOC
∠BOD = 40°
Further, applying the property, “an exterior angle of a triangle is equal to the sum of the two opposite interior angles”, in ΔAOC, we get,
x° = ∠ACO + ∠AOC
x° = 80° + 40°
x° = 120°
Similarly, in ΔBOD
y° = ∠BOD + ∠BDO
y° = 40° + 70°
y° = 110°
Thus,
x° + y° = 120° + 110°
x° + y° = 230°
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.
In a ΔABC, if ∠A=l20° and AB = AC. Find ∠B and ∠C.
In figure, AB = AC and DB = DC, find the ratio ∠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.
If the base of an isosceles triangle is produced on both sides, prove that the exterior angles so formed are equal to each other.
P is a point on the bisector of an angle ∠ABC. If the line through P parallel to AB meets BC at Q, prove that triangle BPQ 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°.
ABC is a triangle and D is the mid-point of BC. The perpendiculars from D to AB and AC are equal. Prove that the triangle is isosceles.
Which of the following statements are true (T) and which are false (F):
If the bisector of the vertical angle of a triangle bisects the base, then the triangle may be isosceles.
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.
In an isosceles triangle ABC with AB = AC, if BD and CE are its altitudes, then BD is …… CE.
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 ……
Is it possible to draw a triangle with sides of length 2 cm, 3 cm and 7 cm?
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.
ABC is a triangle. The bisector of the exterior angle at B and the bisector of ∠C intersect each other at D. Prove that ∠D = \[\frac{1}{2}\] ∠A.
In the given figure, for which value of x is l1 || l2?
The base BC of triangle ABC is produced both ways and the measure of exterior angles formed are 94° and 126°. Then, ∠BAC =
In ∆PQR, if ∠R > ∠Q, then ______.
Is it possible to construct a triangle with lengths of its sides as 9 cm, 7 cm and 17 cm? Give reason for your answer.
