What is the measure of the - D-53- -37- -90- -33- -

The correct option is B 37^ ∘The corresponding sides of Δ ABC and Δ ABD are equal nbsp;by SSS congruency. So, Δ ABC ≅Δ ABD ∠ A +∠ B +∠ C= 180^∘ [Angle sum ...

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Byju's Answer

Standard VIII

Mathematics

Congrueny of Triangles

What is the m...

Question

What is the measure of the $∠ D$ ?

53^{\circ}

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37^{\circ}

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90^{\circ}

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33^{\circ}

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Solution

The correct option is B $37^{\circ}$
The corresponding sides of $Δ A B C$ and $Δ A B D$ are equal by SSS congruency. So,
$Δ A B C ≅ Δ A B D$

$∠ A + ∠ B + ∠ C = 180^{\circ} [A n g l e s u m p r o p e r t y] 53^{\circ} + 90^{\circ} + ∠ C = 180^{\circ} ∠ C = 180^{\circ} - 143^{\circ} ∠ C = 37^{\circ} A s ∠ C = ∠ D [Δ A B C ≅ Δ A B D] ∠ D = 37^{\circ}$

Suggest Corrections

What is the measure of the ∠D?

The correct option is B 37∘The corresponding sides of ΔABC and ΔABD are equal by SSS congruency. So, ΔABC≅ΔABD ∠A+∠B+∠C=180∘[Angle sum property]53∘+90∘+∠C=180∘ ∠C=180∘−143∘ ∠C=37∘As ∠C=∠D [ΔABC≅ΔABD] ∠D=37∘

What is the measure of the $∠ D$ ?