If $∠ A$ and $∠ B$ are equal and supplementary to each other, then find the values of $∠ A$ and $∠ B$ .

∠ A = 100 °, ∠ B = 80 °

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∠ A = 90 °, ∠ B = 90 °

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∠ A = 0 °, ∠ B = 180 °

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∠ A = 45 °, ∠ B = 45 °

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Solution

The correct option is B $∠ A = 90 °, ∠ B = 90 °$
Given: $∠ A$ and $∠ B$ are equal and are supplementary to each other.

$\Rightarrow$ $∠ A + ∠ B = 180^{\circ}$
$\Rightarrow$ $2 \times ∠ A = 180^{\circ}$ $(∵ ∠ A = ∠ B)$
$\Rightarrow$ $∠ A = 90^{\circ}$
$\Rightarrow$ $∠ B = ∠ A = 90^{\circ}$
Thus, $∠ A$ = 90° and $∠ B$ = 90°.

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If ∠ A and ∠ B are equal and supplementary to each other, then find the values of ∠ A and ∠ B.

The correct option is B ∠ A=90°,∠ B=90°Given: ∠A and ∠B are equal and are supplementary to each other. ⇒ ∠A+∠B=180∘ ⇒ 2× ∠A=180∘ (∵∠A=∠B ) ⇒ ∠A=90∘ ⇒ ∠B=∠A=90∘ Thus, ∠A = 90° and ∠B = 90°.

If $∠ A$ and $∠ B$ are equal and supplementary to each other, then find the values of $∠ A$ and $∠ B$ .