Question

find the measure of ∠E​

Answer 1

Answer:

30°

Given:

∆1=AB=5cm,AC=13cm,BAC=60°,ABC=90°

∆2=EF=13cm,DF=5cm,EDF=90°

∆1 is congruent to ∆2 (SSA)

Step-by-step explanation:

In triangle 2 :-

EDF=90°, EFD=60°(Because ∆1 is congruent to ∆2)

Let the angle E be x°

sum of angles of triangle =180°

EDF + EFD + x° = 180°

90°+60°+x° = 180°

150°+x° = 180°

x° = 180°-150°

x° = 30°

Conclusion:

Angle E measures 30°.

Answer 2

Step-by-step explanation:

Using the theorem of Congruent Triangle.

In∆ABC

Given:-

angle BAC=60°

AB=5 cm

AB=5 cm AC=13 cm

Solving:-

BC=√(5²-13²)

BC=√(25-169)

BC=√144

BC=12 cm

In∆ABC

Given:-

DF=5 cm

EF=13 cm

=13 cm Solving:-

DE=√(5²-13²)

DE=√(25-169)

DE=√144

DE=12 cm

In ∆ABC and ∆DEF.

So,

AB=DF

AC=EF

BC=DE

so, ∆ABC is Congruent to ∆DEF(SSS)

So, angle BAC=angle DFE(C.P.C.T.C)

So angle DFE= 60°

In ∆DEF

angle EDF=90°

angle DFE=60°

angle DEF=180°-(90°+60°)(Angle Sum Property)

∠E =180°-150°

∠E =30°

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