Advertisements
Advertisements
Question
Line segments AB and CD intersect at O such that AC || DB. If ∠CAB = 45° and ∠CDB = 55°, then ∠BOD =
Options
100°
80°
90°
135°
Advertisements
Solution
In the given problem, line segment AB and CD intersect at O, such that ,AC || DB , ∠CAB = 45° and ∠CDB = 55° .
We need to find ∠BOD
As AC || DB
Applying the property, “alternate interior angles are equal”, we get,
∠OBD = ∠CAB
∠OBD= 55° .......(1)
Now, using the angle sum property of the triangle
In ΔODB, we get,
∠OBD + ∠ODB + ∠BOD = 180°
55° + 45° + ∠DOB = 180° (using 1)
∠BOD = 180 °- 100°
∠BOD = 80°
Thus,∠BOD = 80°
APPEARS IN
RELATED QUESTIONS
Find the measure of each exterior angle of an equilateral triangle.
Prove that the medians of an equilateral triangle are equal.
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.
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 right angled triangle in which ∠A = 90° and AB = AC. Find ∠B and ∠C.
Which of the following statements are true (T) and which are false (F) :
If the altitude from one vertex of a triangle bisects the opposite side, then the triangle may be isosceles.
Which of the following statements are true (T) and which are false (F)?
Sum of any two sides of a triangle is greater than twice the median drawn to 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.
The sum of any two sides of a triangle is .... than the third side.
Fill in the blank to make the following statement true.
Difference of any two sides of a triangle is........ than the third side.
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, what is z in terms of x and y?
In the given figure, what is the value of x?
In the given figure, if l1 || l2, the value of x is
The angles of a right angled triangle are
In ∆PQR, if ∠R > ∠Q, then ______.
ABC is an isosceles triangle with AB = AC and D is a point on BC such that AD ⊥ BC (Figure). To prove that ∠BAD = ∠CAD, a student proceeded as follows:
In ∆ABD and ∆ACD,
AB = AC (Given)
∠B = ∠C (Because AB = AC)
and ∠ADB = ∠ADC
Therefore, ∆ABD ≅ ∆ACD (AAS)
So, ∠BAD = ∠CAD (CPCT)
What is the defect in the above arguments?
[Hint: Recall how ∠B = ∠C is proved when AB = AC].
