Advertisements
Advertisements
Question
In the given figure, x + y =
Options
270
230
210
190°
Advertisements
Solution
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
RELATED QUESTIONS
In an isosceles triangle ABC, with AB = AC, the bisectors of ∠B and ∠C intersect each other at O. Join A to O. Show that:
- OB = OC
- AO bisects ∠A
In Figure 10.24, AB = AC and ∠ACD =105°, find ∠BAC.
BD and CE are bisectors of ∠B and ∠C of an isosceles ΔABC with AB = AC. Prove that BD = CE.
In an isosceles triangle, if the vertex angle is twice the sum of the base angles, calculate the angles of the triangle.
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 right angled triangle in which ∠A = 90° and AB = AC. Find ∠B and ∠C.
Fill the blank in the following so that the following statement is true.
In a ΔABC if ∠A = ∠C , then AB = ......
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 = ....
In a ΔABC, if ∠B = ∠C = 45°, which is the longest side?
Is it possible to draw a triangle with sides of length 2 cm, 3 cm and 7 cm?
In Fig. 10.131, prove that: (i) CD + DA + AB + BC > 2AC (ii) CD + DA + AB > BC
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.
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.
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 ΔABC, if ∠A = 100°, AD bisects ∠A and AD ⊥ BC. Then, ∠B =
Line segments AB and CD intersect at O such that AC || DB. If ∠CAB = 45° and ∠CDB = 55°, then ∠BOD =
In the given figure, for which value of x is l1 || l2?
In the given figure, the value of x is ______.
If the bisectors of the acute angles of a right triangle meet at O, then the angle at Obetween the two bisectors is
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.
