Q. 124.8( 5 Votes )

# In Fig. 9.41, if *AB* || *DE* and *BD* || *FG* such that ∠*FGH* = 125° and ∠*B* = 55°, find *a* and *y*.

Answer :

Given,

*AB* || *DE* and,

*BD* || *FG*

∠FGH + ∠FGE = 180^{o} (Linear pair)

125^{o} + y = 180^{o}

y = 55^{o}

∠ABC = ∠BDE (Alternate angles)

∠BDF = ∠EFG = 55^{o} (Alternate angles)

∠EFG + ∠FEG = 125^{o} (By exterior angle theorem)

55^{o} + ∠FEG = 125^{o}

∠FEG = x = 70^{o}

Thus, x = 70^{o} and y = 55^{o}.

Rate this question :

Write the sum of the angles of an obtuse triangle.

RD Sharma - MathematicsProve that the angles opposite to equal sides of a triangle are equal

RS Aggarwal & V Aggarwal - MathematicsIf the sides of a triangle are produced in order, then the sum of the three exterior angles so formed is

RD Sharma - MathematicsIn Δ *ABC*, if ∠*A* = 100° *AD* bisects ∠*A* and AD⊥BC. Then, ∠*B* =

D is any point on side AC of a ΔABC with AB = AC. Show that CD < BD.

NCERT Mathematics ExemplarIn a triangle *ABC*, if *AB* = *AC* and AB is produced to *D* such that *BD* = *BC*, find ∠*ACD*: ∠*ADC.*

If the side of a triangle are produced in order, Prove that the sum of the exterior angles so formed is equal to four right angles.

RS Aggarwal & V Aggarwal - Mathematics

*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* = ∠*A.*

In Δ *ABC*, ∠*A*=50° and *BC* is produced to a point *D*. If the bisectors of ∠*ABC* and ∠*ACD* meet at *E*, then ∠*E* =

Compute the value of *x* in each of the following figures:

(i)

(ii)

(iii)

(iv)

RD Sharma - Mathematics