An isosceles triangle has two equal sides and two equal base angles. Let’s denote the vertical angle as \( \theta \) and the base angles as \( \alpha \). Since it is given that one of the base angles is \( \alpha = 48^\circ \), the other base angle is also \( 48^\circ \).
The sum of all interior angles in any triangle is always \( 180^\circ \). Thus, for this isosceles triangle:
\[ \alpha + \alpha + \theta = 180^\circ \]
Substitute the given base angles:
\[ 48^\circ + 48^\circ + \theta = 180^\circ \]
Combine the base angles:
\[ 96^\circ + \theta = 180^\circ \]
To find the value of \( \theta \), subtract \( 96^\circ \) from \( 180^\circ \):
\[ \theta = 180^\circ - 96^\circ \]
\[ \theta = 84^\circ \]
Therefore, the vertical angle of the isosceles triangle is \( 84^\circ \).
Calculate the vertical angle of an isosceles triangle if one of its base angle is 48degree
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