Advertisements
Advertisements
Question
Find the measure of each exterior angle of an equilateral triangle.
Advertisements
Solution
Given to find the measure of each exterior angle of an equilateral triangle consider an
equilateral triangle ABC.
We know that for an equilateral triangle
AB = BC = CA and
`∠ABC =∠BCA =∠CAB=180^@/3=60^@` .......1
Now,
Extend side BC to D, CA to E and AB to F.
Here
BCD is a straight line segment
`⇒∠BCD = Straight angle 180^@`
`∠BCA+∠ACD=180^@`
`⇒60^@+∠ACD=180^@`
Similarly, we can find ∠FAB and ∠FBC also as `120^@` because ABC is an equilateral
triangle
`∴∠ACD =∠EAB =∠FBC =120^@`
Hence, the median of each exterior angle of an equilateral triangle is `120^@`
APPEARS IN
RELATED QUESTIONS
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.
BD and CE are bisectors of ∠B and ∠C of an isosceles ΔABC with AB = AC. Prove that BD = CE.
PQR is a triangle in which PQ = PR and S is any point on the side PQ. Through S, a line is drawn parallel to QR and intersecting PR at T. Prove that PS = PT.
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.
ABC is a right angled triangle in which ∠A = 90° and AB = AC. Find ∠B and ∠C.
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.
Sides opposite to equal angles of a triangle are ......
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, if ∠A = 40° and ∠B = 60°. Determine the longest and shortest sides of the triangle.
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 sides of a triangle are unequal, then the larger side has .... angle opposite to it.
If the angles of a triangle are in the ratio 2 : 1 : 3, then find the measure of smallest angle.
In a ΔABC, if ∠A = 60°, ∠B = 80° and the bisectors of ∠B and ∠C meet at O, then ∠BOC =
In the given figure, if EC || AB, ∠ECD = 70° and ∠BDO = 20°, then ∠OBD is
In the given figure, x + y =
In the given figure, what is z in terms of x and y?
The base BC of triangle ABC is produced both ways and the measure of exterior angles formed are 94° and 126°. Then, ∠BAC =
D is a point on the side BC of a ∆ABC such that AD bisects ∠BAC. Then ______.
