Question

The two adjacent angles of a quadrilateral are 67° & 105°. The other two adjacent angles are equal. what is the measure of each of these equal angles?

Answer 1

⇝Given :-

Two adjacent angles of a quadrilateral :

• 1st angle = 67°
• 2nd angle = 105°

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⇝To Find :-

Find other two adjacent angle :

• 3rd angle = ?
• 4th angle = ?

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⇝Solution :-

❒We know that :

Sum of all adjacent angles of a quadrilateral is 360°.

❒Let :

The two equal angles be x°.

❒Solving starts :

${\twoheadrightarrow{\sf{67° + 105° + x + x = 360°}}}$

${\twoheadrightarrow{\sf{172° + 2x = 360°}}}$

${\twoheadrightarrow{\sf{2x = 360° - 172°}}}$

${\twoheadrightarrow{\sf{2x = 188°}}}$

${\twoheadrightarrow{\sf{X = {\cancel\frac{188}{2} }}}}$

${\large{\blue{:{\longmapsto{\pink{\underline{\boxed{\mathbb{\bf{X = 94° }}}}}}}}}}</p><p>$

❒Hence :

${\green{➳{\red{\bf{Angle \: 3 = X = 94°}}}}}$

${\green{➳{\red{\bf{Angle \: 4 = X = 94°}}}}}$

❒For Verification :

${\orange{\leadsto{\sf{Angle 1 + Angle 2 + Angle 3 + Angle 4 = 360°}}}}$

${\orange{\leadsto{\sf{67° + 105° + 94° + 94° = 360°}}}}$

${\purple{\bf{360° = 360°}}}$

${\purple{\bf{LHS = RHS}}}$

$\: \: \: \: \: \: \: \: \: {\orange{\underbrace{\overbrace{\green{\mathfrak{Hence , verified}}}}}}$

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