Advertisements
Advertisements
Question
If the bisectors of the base angles of a triangle enclose an angle of 135°, prove that the triangle is a right triangle.
Advertisements
Solution
Given the bisectors the base angles of an triangle enclose an angle of `135^@`
i.e., ∠BOC=`135^@`
But, W.K.T
`∠ BOC=90^@+1/2∠B`
⇒ `135^@=90^@+1/2∠A`
⇒`1/2∠A=135^@-90^@`
⇒`∠A=45^@(2)`
⇒`∠A=90^@`
∴ ΔABC is right angled triangle right angled at A.
APPEARS IN
RELATED QUESTIONS
Can a triangle have All angles more than 60°? Justify your answer in case.
In Δ ABC, BD⊥ AC and CE ⊥ AB. If BD and CE intersect at O, prove that ∠BOC = 180° − A.
In ΔABC, ∠B = ∠C and ray AX bisects the exterior angle ∠DAC. If ∠DAX = 70°, then ∠ACB =
If the sides of a triangle are produced in order, then the sum of the three exterior angles so formed is
If the angles of a triangle are equal, find its angles.
Find the value of the angle in the given figure:
One angle of a right-angled triangle is 70°. Find the other acute angle.
As shown in the figure, Avinash is standing near his house. He can choose from two roads to go to school. Which way is shorter? Explain why.
AB and CD are the smallest and largest sides of a quadrilateral ABCD. Out of ∠B and ∠D decide which is greater.
Can we have two acute angles whose sum is an acute angle? Why or why not?
