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Alecsey [184]
3 years ago
14

Right triangle ABC and right triangle ACD overlap as shown below. Angle DAC measures 20 degrees and angel BCA measures 30 degree

s. What are the values of X and Y?

Mathematics
1 answer:
alexdok [17]3 years ago
6 0

The image of the question is attached below.

Given:

m∠DAC = 20° and m∠BCA = 30°

m∠ABC = 90° and m∠CDA = 90°

To find:

The value of x and y.

Solution:

In right triangle ABC,

m∠BAC = x° + 20°

Sum of the interior angles of a triangle = 180°

m∠BAC +m∠ABC + m∠BCA = 180°

x° + 20° + 90° + 30° = 180°

x° + 140° = 180°

Subtract 140° from both sides.

x° + 140° - 140° = 180° - 140°

x° = 40°

In right triangle ADC,

m∠ACD = y° + 30°

Sum of the interior angles of a triangle = 180°

m∠ACD +m∠CDA + m∠DAC = 180°

y° + 30° + 90° + 20° = 180°

y° + 140° = 180°

Subtract 140° from both sides.

y° + 140° - 140° = 180° - 140°

y° = 40°

The value of x is 40 and y is 40.

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