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In the triangle below, if < C = 62 °, what is the measure of angle B?

In The Triangle Below If Lt C 62 What Is The Measure Of Angle B class=

Sagot :

In the given triangle ABC

[tex]BA=BC[/tex]

Then the triangle is isosceles

In the isosceles triangle, the base angles are equal

Since [tex]m\angle A=m\angle C[/tex]Since m[tex]m\angle A=62^{\circ}[/tex]In any triangle the sum of angles is 180 degrees, then

[tex]m\angle A+m\angle B+m\angle C=180^{\circ}[/tex]

Substitute angles A and C by 62

[tex]\begin{gathered} 62+m\angle B+62=180 \\ \\ m\angle B+124=180 \end{gathered}[/tex]

Subtract 124 from both sides

[tex]\begin{gathered} m\angle B+124-124=180-124 \\ \\ m\angle B=56^{\circ} \end{gathered}[/tex]

The answer is b

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