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

As CD || BA [Given]

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

We can write ED || BA

⇒ ∠ECB = ∠CBA [Alternate angles are equal]

⇒ ∠CBA = 75°

Since, ABCD is a parallelogram, we have

⇒ ∠DAB + ∠CBA = 180° (AD || BC, sum of co-int ∠s = 180°)

⇒ (x + 66°) + 75° = 180°

⇒ x + 141° = 180°

⇒ x = 180° – 141°

⇒ x = 39° … (i)

Now, in ∆AMB

⇒ x + 30° + ∠AMB = 180° [Angles sum property of a triangle]

39° + 30° + ∠AMB = 180° [From (i)]

69° + ∠AMB + 180°

∠AMB = 180° – 69° = 111°

Since, ∠AMB = y [Vertically opposite angles are equal]

⇒ y = 111°

Hence, x = 39° and y = 111°

Answered By

3 Likes


Related Questions