Advertisements
Advertisements
प्रश्न
Line segments AB and CD intersect at O such that AC || DB. If ∠CAB = 45° and ∠CDB = 55°, then ∠BOD =
विकल्प
100°
80°
90°
135°
Advertisements
उत्तर
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
संबंधित प्रश्न
ABC and DBC are two isosceles triangles on the same base BC (see the given figure). Show that ∠ABD = ∠ACD.
Prove that the medians of an equilateral triangle are equal.
In an isosceles triangle, if the vertex angle is twice the sum of the base angles, calculate the angles of the triangle.
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.
In right triangles ABC and DEF, if hypotenuse AB = EF and side AC = DE, then ΔABC ≅ Δ ……
In ΔABC, if ∠A = 40° and ∠B = 60°. Determine the longest and shortest sides of the triangle.
In ΔABC, side AB is produced to D so that BD = BC. If ∠B = 60° and ∠A = 70°, prove that: (i) AD > CD (ii) AD > AC
Is it possible to draw a triangle with sides of length 2 cm, 3 cm and 7 cm?
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.
Fill in the blank to make the following statement true.
The sum of any two sides of a triangle is .... than the third side.
If the angles A, B and C of ΔABC satisfy the relation B − A = C − B, then find the measure of ∠B.
In ΔABC, if ∠A = 100°, AD bisects ∠A and AD ⊥ BC. Then, ∠B =
The side BC of ΔABC is produced to a point D. The bisector of ∠A meets side BC in L. If ∠ABC = 30° and ∠ACD = 115°, then ∠ALC = ______.
In ∆PQR, ∠R = ∠P and QR = 4 cm and PR = 5 cm. Then the length of PQ is ______.
Two sides of a triangle are of lengths 5 cm and 1.5 cm. The length of the third side of the triangle cannot be ______.
In triangles ABC and PQR, AB = AC, ∠C = ∠P and ∠B = ∠Q. The two triangles are ______.
In ∆PQR, ∠P = 70° and ∠R = 30°. Which side of this triangle is the longest? 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.
Show that in a quadrilateral ABCD, AB + BC + CD + DA < 2(BD + AC)
