Advertisements
Advertisements
प्रश्न
In the given figure, if l1 || l2, the value of x is
विकल्प
\[22\frac{1}{2}\]
30
45
60
Advertisements
उत्तर
In the given problem, l1 || l2
We need to find the value of x
Here, as l1 || l2 , using the property, “consecutive interior angles are supplementary”, we get
∠DAC + ∠ECA = 180°
a + a+ b+ b =180°
2a + 2b = 180°
`a + b = (180°)/2`
a + b = 90° ..........(1)
Further, applying angle sum property of the triangle
In ΔABC
∠BAC + ∠BCA + ∠ABC =180°
a + b + ∠ABC = 180°
90 + ∠ABC = 180° (using 1)
∠ABC = 180° - 90°
∠ABC = 90°
Now, AB is a straight line, so using the property, “angles forming a linear pair are supplementary”, we get,
x + x + ∠ABC = 180°
2x + 90° = 180°
2x = 180° - 90°
`x = (90°)/2`
x = 45°
Thus, x = 45°
APPEARS IN
संबंधित प्रश्न
ABC is a triangle in which altitudes BE and CF to sides AC and AB are equal (see the given figure). Show that
- ΔABE ≅ ΔACF
- AB = AC, i.e., ABC is an isosceles triangle.
ΔABC is an isosceles triangle in which AB = AC. Side BA is produced to D such that AD = AB (see the given figure). Show that ∠BCD is a right angle.
In Figure AB = AC and ∠ACD =105°, find ∠BAC.
Find the measure of each exterior angle of an equilateral triangle.
Determine the measure of each of the equal angles of a right-angled isosceles triangle.
AB is a line seg P and Q are points on opposite sides of AB such that each of them is equidistant from the points A and B (See Fig. 10.26). Show that the line PQ is perpendicular bisector of AB.
In Figure 10.24, AB = AC and ∠ACD =105°, find ∠BAC.
P is a point on the bisector of an angle ∠ABC. If the line through P parallel to AB meets BC at Q, prove that triangle BPQ is isosceles.
In a ΔPQR, if PQ = QR and L, M and N are the mid-points of the sides PQ, QR and RP
respectively. Prove that LN = MN.
Fill the blank in the following so that the following statement is true.
Angle opposite to equal sides of a triangle are .....
O is any point in the interior of ΔABC. Prove that
(i) AB + AC > OB + OC
(ii) AB + BC + CA > OA + QB + OC
(iii) OA + OB + OC >` 1/2`(AB + BC + CA)
Which of the following statements are true (T) and which are false (F)?
Difference of any two sides of a triangle is equal to the third side.
In the given figure, for which value of x is l1 || l2?
In the given figure, what is y in terms of x?
In the given figure, the value of x is ______.
In the given figure, if BP || CQ and AC = BC, then the measure of x is
In ∆ABC, BC = AB and ∠B = 80°. Then ∠A is equal to ______.
AD is a median of the triangle ABC. Is it true that AB + BC + CA > 2AD? 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.
