Advertisements
Advertisements
Question
ABC is a triangle in which ∠A — 72°, the internal bisectors of angles B and C meet in O.
Find the magnitude of ∠BOC.
Advertisements
Solution
Given,
ABC is a triangle
`∠ A=72^@` and internal bisector of angles B and C meeting O
In` Δ ABC = ∠ A+∠ B+∠ C=180^@`
⇒`72^@+∠ B+∠ C=180^@`
⇒`∠ B+∠C =180^@-72^@ ` divide both sides by ‘2’
⇒`∠ B/2+∠ C/2=108^@/2` ..................(1)
⇒`∠ OBC +∠ OCB =54^@` ...................(1)
Now in `Δ BOC⇒ ∠OBC +∠ OCB +∠ BOC = 180^@`
⇒ `54^@+∠BOC=180^@`
⇒ `∠BOC=180^@-54^@=126^@`
∴` ∠ BOC=126^@`
APPEARS IN
RELATED QUESTIONS
In a ΔABC, ∠ABC = ∠ACB and the bisectors of ∠ABC and ∠ACB intersect at O such that ∠BOC = 120°. Show that ∠A = ∠B = ∠C = 60°.
Can a triangle have All angles more than 60°? Justify your answer in case.
Can a triangle have All angles equal to 60°? Justify your answer in case.
If the bisector of the exterior vertical angle of a triangle be parallel to the base. Show that the triangle is isosce
Compute the value of x in the following figure:
In the given figure, AB || DE. Find ∠ACD.
Fill in the blank to make the following statement true:
A triangle cannot have more than ...... right angles.
The length of the sides of the triangle is given. Say what types of triangles they are 4.3 cm, 4.3 cm, 4.3 cm.
The number of angles in the following figure is ______.
How many angles are there inside a triangle?
