Mathematics
Find the size of each lettered angle in the following figure.
Rectilinear Figures
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Answer
As CD || BA [Given]
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°
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