KnowledgeBoat Logo

Mathematics

Find the size of each lettered angle in the following figure.

Find the size of each lettered angle in the figure. Rectilinear Figures, ML Aggarwal Understanding Mathematics Solutions ICSE Class 9.

Rectilinear Figures

1 Like

Answer

In △ADC,

AD = CD (Given)

Find the size of each lettered angle in the figure. Rectilinear Figures, ML Aggarwal Understanding Mathematics Solutions ICSE Class 9.

∠DAC = ∠DCA = 42° (Opposite angles of equal sides are equal).

⇒ ∠DAC + ∠DCA + ∠ADC = 180°

⇒ 42° + 42° + y = 180°

⇒ y + 84° = 180°

⇒ y = 96°

In △AOB and △COB,

AO = OC (Diagonals bisect each other)

AB = BC (Given)

∠AOB = ∠COB = 90° (Diagonals are perpendicular to each other)

Hence, △AOB ≅ △COB by RHS congruence rule.

By C.P.C.T. we get,

⇒ ∠ABO = ∠CBO = 26°

In △AOB,

⇒ ∠AOB + ∠ABO + ∠OAB = 180° (Sum of angles of triangle = 180°)

⇒ 90° + 26° + x = 180°

⇒ 116° + x = 180°

⇒ x = 180° - 116° = 64°

Hence, x = 64° and y = 96°.

Answered By

3 Likes


Related Questions