Question

An isosceles triangle has an angle that measures 38degrees. What measures are possible for the other two angles? Choose all that apply.

Answer 1

• 71° and 71°.

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Explanation:

The triangle having two sides equal along with one different side is called an isosceles triangle.

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• So, Let us assume the other sides (two equal sides) of the isosceles triangle as x. As the different side is already given in the question.

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We know that,

• The sum of all angles of a triangle is 180°

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So, According to the question :

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`{\longrightarrow \it\qquad { \ { { 38 \: }^( \circ) + x + x = 180{}^( \circ) }}}`

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`{\longrightarrow \it\qquad { \ { { 38 \: }^( \circ) + 2x = 180{}^( \circ) }}}`

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`{\longrightarrow \it\qquad { \ { 2x = 180{}^( \circ) - { 38 \: }^( \circ)}}}`

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`{\longrightarrow \it\qquad { \ { 2x = 142{}^( \circ) }}}`

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`{\longrightarrow \it\qquad { \ { x = \frac{142{}^( \circ)}{2} }}}`

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`{\longrightarrow \it\qquad { \pmb { x = 71^( \circ) }}}`

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Therefore,

• The measure of the two other angles of the isosceles triangle are 71° and 71°.