Advertisements
Advertisements
Question
In the given figure, if l1 || l2, the value of x is
Options
\[22\frac{1}{2}\]
30
45
60
Advertisements
Solution
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
RELATED QUESTIONS
In an isosceles triangle ABC, with AB = AC, the bisectors of ∠B and ∠C intersect each other at O. Join A to O. Show that:
- OB = OC
- AO bisects ∠A
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.
ABC and DBC are two isosceles triangles on the same base BC (see the given figure). Show that ∠ABD = ∠ACD.
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 DB = DC, find the ratio ∠ABD : ∠ACD
Two lines AB and CD intersect at O such that BC is equal and parallel to AD. Prove that the lines AB and CD bisect at O.
Prove that the medians of an equilateral triangle are equal.
In Figure 10.24, AB = AC and ∠ACD =105°, find ∠BAC.
Find the measure of each exterior angle of an equilateral triangle.
Two lines AB and CD intersect at O such that BC is equal and parallel to AD. Prove that the lines AB and CD bisect at O.
Angles A, B, C of a triangle ABC are equal to each other. Prove that ΔABC is equilateral.
ABC is a triangle in which BE and CF are, respectively, the perpendiculars to the sides AC and AB. If BE = CF, prove that ΔABC is isosceles
Which of the following statements are true (T) and which are false (F):
If the bisector of the vertical angle of a triangle bisects the base, then the triangle may be isosceles.
Fill the blank in the following so that the following statement is true.
In an isosceles triangle ABC with AB = AC, if BD and CE are its altitudes, then BD is …… CE.
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
In Fig. 10.131, prove that: (i) CD + DA + AB + BC > 2AC (ii) CD + DA + AB > BC
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.
In the given figure, if AB ⊥ BC. then x =
In the given figure, if BP || CQ and AC = BC, then the measure of x is
Find all the angles of an equilateral triangle.
