Advertisements
Advertisements
Question
In the given figure, if EC || AB, ∠ECD = 70° and ∠BDO = 20°, then ∠OBD is
Options
20°
50°
60°
70°
Advertisements
Solution
In the given figure, EC || AB,∠ECD = 70° and ∠BDO= 20°. We need to find ∠OBD.
Here, EC || AB and CD is the transversal, so using the property, “corresponding angles are equal”, we get
∠AOD = ∠ECD
∠AOD = 70°
Also, using the property, “an exterior angle of a triangle is equal to the sum of the two opposite interior angles”, in ΔOBD, we get,
∠AOD = ∠OBD + ∠BDO
70° = ∠OBD + 20°
∠OBD = 70° - 20°
∠OBD = 50°
Thus,∠OBD = 50° .
APPEARS IN
RELATED QUESTIONS
In figure, AB = AC and DB = DC, find the ratio ∠ABD : ∠ACD
In Fig. 10.40, it is given that RT = TS, ∠1 = 2∠2 and ∠4 = 2∠3. Prove that ΔRBT ≅ ΔSAT
In a ΔABC, if ∠A=l20° and AB = AC. Find ∠B and ∠C.
If the base of an isosceles triangle is produced on both sides, prove that the exterior angles so formed are equal to each other.
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):
Sides opposite to equal angles of a triangle may be unequal
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.
Sides opposite to equal angles of a triangle are ......
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)
Which of the following statements are true (T) and which are false (F)?
Sum of the three sides of a triangle is less than the sum of its three 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.
Write the sum of the angles of an obtuse triangle.
If the angles of a triangle are in the ratio 2 : 1 : 3, then find the measure of smallest angle.
In the given figure, AB and CD are parallel lines and transversal EF intersects them at Pand Q respectively. If ∠APR = 25°, ∠RQC = 30° and ∠CQF = 65°, then
In a ΔABC, ∠A = 50° and BC is produced to a point D. If the bisectors of ∠ABC and ∠ACDmeet at E, then ∠E =
AD is a median of the triangle ABC. Is it true that AB + BC + CA > 2AD? Give reason for your answer.
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.
In the following figure, D and E are points on side BC of a ∆ABC such that BD = CE and AD = AE. Show that ∆ABD ≅ ∆ACE.
Bisectors of the angles B and C of an isosceles triangle ABC with AB = AC intersect each other at O. Show that external angle adjacent to ∠ABC is equal to ∠BOC
