Advertisements
Advertisements
प्रश्न
In Figure AB = AC and ∠ACD =105°, find ∠BAC.
Advertisements
उत्तर
Consider the given figure
We have,
AB = AC and ∠ACD =105^@
Since,
∠BCD = 180° = Straight angle
∠BCA + ∠ACD = 180°
∠BCA +105° = 180°
∠BCA = 180° -105° ⇒ ∠BCA = 75° .......1
And also,
ΔABC is an isosceles triangle [∵AB = AC]
⇒ ∠ABC = ∠ACB
From (1), we have [Angles opposite to equal sides are equal]
∠ACB = 75° ⇒∠ABC = ∠ACB = 75°
And also,
Sum of interior angles of a triangle = 180°
⇒∠ABC = ∠BCA + ∠CAB = 180°
⇒ 75° + 75° + ÐCAB = 180°
⇒ 150° +∠BAC = 180°⇒ ∠BAC = 180° -150° = 30°
∠BAC=30°
APPEARS IN
संबंधित प्रश्न
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
In a ΔABC, if AB = AC and ∠B = 70°, find ∠A.
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°.
In a ΔABC, if ∠B = ∠C = 45°, which is the longest side?
In Fig. 10.131, prove that: (i) CD + DA + AB + BC > 2AC (ii) CD + DA + AB > BC
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.
In a right triangle the hypotenuse is the .... 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.
Difference of any two sides of a triangle is........ than the third side.
In the given figure, if AB || DE and BD || FG such that ∠FGH = 125° and ∠B = 55°, find x and y.
In ΔABC, if ∠A = 100°, AD bisects ∠A and AD ⊥ BC. Then, ∠B =
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 BP || CQ and AC = BC, then the measure of x is
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 = ______.
D is a point on the side BC of a ∆ABC such that AD bisects ∠BAC. Then ______.
Is it possible to construct a triangle with lengths of its sides as 8 cm, 7 cm and 4 cm? Give reason for your answer.
CDE is an equilateral triangle formed on a side CD of a square ABCD (Figure). Show that ∆ADE ≅ ∆BCE.
Bisectors of the angles B and C of an isosceles triangle ABC with AB = AC intersect each other at O. Show that external angle adjacent to ∠ABC is equal to ∠BOC
