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
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.
Determine the measure of each of the equal angles of a right-angled isosceles triangle.
In Fig. 10.40, it is given that RT = TS, ∠1 = 2∠2 and ∠4 = 2∠3. Prove that ΔRBT ≅ ΔSAT
In Fig. 10.23, PQRS is a square and SRT is an equilateral triangle. Prove that
(i) PT = QT (ii) ∠TQR = 15°
If the bisector of the exterior vertical angle of a triangle be parallel to the base. Show that the triangle is isosceles.
In an isosceles triangle, if the vertex angle is twice the sum of the base angles, calculate the angles of the triangle.
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):
Angles opposite to equal sides of a triangle are equal
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.
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 = ....
Which of the following statements are true (T) and which are false (F)?
If two angles of a triangle are unequal, then the greater angle has the larger side opposite to it.
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.
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 the given figure, if AB || DE and BD || FG such that ∠FGH = 125° and ∠B = 55°, find x and y.
In ∆ABC, AB = AC and ∠B = 50°. Then ∠C is equal to ______.
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 ______.
AD is a median of the triangle ABC. Is it true that AB + BC + CA > 2AD? Give reason for your answer.
CDE is an equilateral triangle formed on a side CD of a square ABCD (Figure). Show that ∆ADE ≅ ∆BCE.
Show that in a quadrilateral ABCD, AB + BC + CD + DA > AC + BD
