Find x, y, z (whichever is required) from the figure.

1.	Find x, y, z (whichever is required) from the figure.
Answer» We know that the sum of all the angles of a triangle is equal to 180°. Therefore, for △ABD: ∠ABD +∠ADB + ∠BAD = 180° (Sum of the angles of △ABD) 50° + x + 50° = 180° 100° + x = 180° x = 180° – 100° x = 80° For △ ABC: ∠ABC + ∠ACB + ∠BAC = 180° (Sum of the angles of △ABC) 50° + z + (50° + 30°) = 180° 50° + z + 50° + 30° = 180° z = 180° – 130° z = 50° Using the same argument for △ADC: ∠ADC + ∠ACD + ∠DAC = 180° (Sum of the angles of △ADC) y + z + 30° = 180° y + 50° + 30° = 180° (z = 50°) y = 180° – 80° y = 100° Therefore, we can conclude that the required angles are 80°, 50° and 100°.

Answer»

We know that the sum of all the angles of a triangle is equal to 180°.

Therefore, for △ABD:

∠ABD +∠ADB + ∠BAD = 180° (Sum of the angles of △ABD)

50° + x + 50° = 180°

100° + x = 180°

x = 180° – 100°

x = 80°

For △ ABC:

∠ABC + ∠ACB + ∠BAC = 180° (Sum of the angles of △ABC)

50° + z + (50° + 30°) = 180°

50° + z + 50° + 30° = 180°

z = 180° – 130°

z = 50°

Using the same argument for △ADC:

∠ADC + ∠ACD + ∠DAC = 180° (Sum of the angles of △ADC)

y + z + 30° = 180°

y + 50° + 30° = 180° (z = 50°)

y = 180° – 80°

y = 100°

Therefore, we can conclude that the required angles are 80°, 50° and 100°.

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