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

1.	Find x, y, z (whichever is required) from the figure.
Answer» We can see that in △ADC, ∠ADC is equal to 90°. (△ADC is a right triangle) We also know that the sum of all the angles of a triangle is equal to 180°. Which means: 45° + 90° + y = 180° (Sum of the angles of △ADC) 135° + y = 180° y = 180° – 135°. y = 45°. We can also say that in △ ABC, ∠ABC + ∠ACB + ∠BAC is equal to 180°. (Sum of the angles of △ABC) 40° + y + (x + 45°) = 180° 40° + 45° + x + 45° = 180° (y = 45°) x = 180° –130° x = 50° Therefore, we can say that the required angles are 45° and 50°.

Answer»

We can see that in △ADC, ∠ADC is equal to 90°.

(△ADC is a right triangle)

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

Which means: 45° + 90° + y = 180° (Sum of the angles of △ADC)

135° + y = 180°

y = 180° – 135°.

y = 45°.

We can also say that in △ ABC, ∠ABC + ∠ACB + ∠BAC is equal to 180°.

(Sum of the angles of △ABC)

40° + y + (x + 45°) = 180°

40° + 45° + x + 45° = 180° (y = 45°)

x = 180° –130°

x = 50°

Therefore, we can say that the required angles are 45° and 50°.

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