Question

 If the vertical angle of an isosceles triangle is 40 degree then find the measure of other two angles. OR In the figure given below POQ is a line, ∠POR = 4x and ∠QOR = 2x then,find the value of x. 

Answer 1

Given :- If the vertical angle of an isosceles triangle is 40 degree then find the measure of other two angles.

Solution :-

from fig(i) , we have ,

→ ∠BAC = 40°

→ AB = AC .

So,

→ ∠ABC = ∠ACB .(angle opposite to equal sides are equal.)

then,

→ ∠BAC + ∠ABC + ∠ACB = 180° (angle sum property.)

→ 40° + ∠ABC + ∠ABC = 180°

→ 2∠ABC = 180° - 40°

→ 2∠ABC = 140°

→ ∠ABC = 70° .

therefore,

→ ∠ABC = ∠ACB = 70° (Ans.)

________________

Given :- In the figure given below POQ is a line, ∠POR = 4x and ∠QOR = 2x then,find the value of x. ?

Solution :-

from fig(ii), we have,

→ POQ is a line.

→ ∠POR = 4x

→ ∠QOR = 2x

So,

→ ∠POR + ∠QOR = 180° . (since , POQ is a straight line , Linear pair angles .)

then,

→ 4x + 2x = 180°

→ 6x = 180°

→ x = 30° (Ans.)

_____________________

Learn more :-

ABCD is a rhombus with A = 60° , BC = (3x+5)cm , CD =(6x-10)cm and AC =(3y-1)cm. Find

x and y.

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3.

In the fig, AB || CD,FIND x.(Hint:Prove that AOB-COD).

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