Advertisements
Advertisements
प्रश्न
In the given figure, if AB || DE and BD || FG such that ∠FGH = 125° and ∠B = 55°, find x and y.
Advertisements
उत्तर
In the given figure,,,and AB ||DE ,BD || FG , ∠FGH =125° and ∠B = 55°
We need to find the value of x and y
Here, as AB || DE and BD is the transversal, so according to the property, “alternate interior angles are equal”, we get
∠D = ∠B
∠D = 55° ............. (1)
Similarly, as BD || FG and DF is the transversal
∠D = ∠F
∠F = 55° (Using 1)
Further, EGH is a straight line. So, using the property, angles forming a linear pair are supplementary
∠FGE + ∠FGH = 180°
y + 125° = 180°
y = 180° - 125°
y = 55°
Also, using the property, “an exterior angle of a triangle is equal to the sum of the two opposite interior angles”, we get,
In ΔEFG with ∠ FGH as its exterior angle
ext. ∠FGH = ∠F + ∠E
125° = 55° + x
x = 125° - 55°
x = 70°
Thus, x = 70° and y = 55°
APPEARS IN
संबंधित प्रश्न
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.
Show that the angles of an equilateral triangle are 60° each.
Find the measure of each exterior angle of an equilateral triangle.
Prove that the medians of an equilateral triangle are equal.
If the bisector of the exterior vertical angle of a triangle be parallel to the base. Show that the triangle is isosceles.
Prove that each angle of an equilateral triangle is 60°.
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°.
Fill the blank in the following so that the following statement is true.
In an equilateral triangle all angles are .....
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)?
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.
If two sides of a triangle are unequal, then the larger side has .... angle opposite to it.
Line segments AB and CD intersect at O such that AC || DB. If ∠CAB = 45° and ∠CDB = 55°, then ∠BOD =
If the measures of angles of a triangle are in the ratio of 3 : 4 : 5, what is the measure of the smallest angle of the triangle?
In the given figure, if AB ⊥ BC. then x =
In the given figure, what is z in terms of x and y?
In ∆PQR, ∠R = ∠P and QR = 4 cm and PR = 5 cm. Then the length of PQ is ______.
In ∆PQR, ∠P = 70° and ∠R = 30°. Which side of this triangle is the longest? 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.
CDE is an equilateral triangle formed on a side CD of a square ABCD (Figure). Show that ∆ADE ≅ ∆BCE.
