And hence - DECA- 65- and 35-B- 95- and 35-C- 75- and 45-D- 65- and 25-

The correct option is D 65^∘ and 25^∘ ∠ DCE + ∠ DCB = 180^∘ ∠ DCE = 180^∘ ∠ DCB = 180^∘ 115^∘ = 65^∘ ∠ DEC + ∠ DCE = 90^∘ Since it is right angled triang ...

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Byju's Answer

Standard VIII

Mathematics

Exterior Angle Theorem

and hence ∠ D...

Question

Find the measure of $∠ D C E$ and hence $∠$ DEC

$65^{\circ}$ and $35^{\circ}$

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$95^{\circ}$ and $35^{\circ}$

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$75^{\circ}$ and $45^{\circ}$

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$65^{\circ}$ and $25^{\circ}$

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Solution

The correct option is D
$65^{\circ}$ and $25^{\circ}$

$∠ D C E + ∠ D C B = 180^{\circ}$

$∠ D C E = 180^{\circ} - ∠ D C B$

= $180^{\circ} - 115^{\circ}$

= $65^{\circ}$

$∠ D E C + ∠ D C E = 90^{\circ}$
Since it is right angled triangle, the remaining two angles will be complementary

$∠ D E C = 90^{\circ} - 65^{\circ}$

= $25^{\circ}$

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Find the measure of ∠DCE and hence ∠DEC

The correct option is D 65∘ and 25∘ ∠DCE+∠DCB=180∘ ∠DCE=180∘−∠DCB = 180∘−115∘ = 65∘ ∠DEC+∠DCE=90∘ Since it is right angled triangle, the remaining two angles will be complementary ∠DEC=90∘−65∘ = 25∘

Find the measure of $∠ D C E$ and hence $∠$ DEC