Advertisements
Advertisements
Question
The vertical angle of an isosceles triangle is 100°. Find its base angles.
Advertisements
Solution
Consider an isosceles ΔABC such that AB= AC
Given that vertical angle A is 100°. Given to find the base angles
SinceΔABC is isosceles
∠B = ∠C [Angles opposite to equal angle are equal]
And also ,
Sum of the interior angle of a triangle = 180°
⇒∠Aa+∠B+∠C=180°
⇒100°+∠B+∠B=180°
⇒2∠B=180°-100° ⇒2∠B=80°
⇒∠B=40 °
⇒∠B=∠C=40°
APPEARS IN
RELATED QUESTIONS
Determine the measure of each of the equal angles of a right-angled isosceles triangle.
In a ΔABC, if ∠A=l20° and AB = AC. Find ∠B and ∠C.
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.
BD and CE are bisectors of ∠B and ∠C of an isosceles ΔABC with AB = AC. Prove that BD = CE.
In a ΔABC, it is given that AB = AC and the bisectors of ∠B and ∠C intersect at O. If M is a point on BO produced, prove that ∠MOC = ∠ABC.
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.
Angles A, B, C of a triangle ABC are equal to each other. Prove that ΔABC is equilateral.
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.
Which of the following statements are true (T) and which are false (F)?
Sum of any two sides of a triangle is greater than the third side.
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.
ABC is a triangle. The bisector of the exterior angle at B and the bisector of ∠C intersect each other at D. Prove that ∠D = \[\frac{1}{2}\] ∠A.
In the given figure, if AB || DE and BD || FG such that ∠FGH = 125° and ∠B = 55°, find x and y.
In the given figure, if BP || CQ and AC = BC, then the measure of x is
In the given figure, AB and CD are parallel lines and transversal EF intersects them at Pand Q respectively. If ∠APR = 25°, ∠RQC = 30° and ∠CQF = 65°, then
D is a point on the side BC of a ∆ABC such that AD bisects ∠BAC. Then ______.
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 ______.
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
