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Standard VII

Mathematics

Angle Sum Property

ABC is an iso...

Question

$△ A B C$ is an isosceles triangle with base angles $50^{o}$ each. On sides $A C$ and $A B$ , equilaterales triangles are drawn (See figure).
Find $∠ E B C, ∠ D C B, ∠ E A C$

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Solution

R.E.F image
$∠$ $E B C =$ $∠$ $E B A$ + $∠$ $A B C$ = $60^{\circ} + 50^{\circ} = 110^{\circ}$
$∠ D C B = ∠ D C A + ∠ A C B = 60^{\circ} + 50^{\circ} = 110^{\circ}$
$∠ B A C = 180^{\circ} - 50^{\circ} - 50^{\circ}$
$= 80^{\circ}$
$∠ E A C = ∠ E A B + ∠ B A C = 60^{\circ} + 80^{\circ} = 140^{\circ}$

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△ABC is an isosceles triangle with base angles 50o each. On sides AC and AB, equilaterales triangles are drawn (See figure).Find ∠EBC,∠DCB,∠EAC

R.E.F image∠ EBC=∠ EBA+∠ ABC=60∘+50∘=110∘ ∠DCB=∠DCA+∠ACB=60∘+50∘=110∘ ∠BAC=180∘−50∘−50∘ =80∘ ∠EAC=∠EAB+∠BAC=60∘+80∘=140∘

$△ A B C$ is an isosceles triangle with base angles $50^{o}$ each. On sides $A C$ and $A B$ , equilaterales triangles are drawn (See figure).
Find $∠ E B C, ∠ D C B, ∠ E A C$