Question

in the given,AB us the diameter of the circle.DC is parallel to AB and angle CAB=35°.find :i)angle ADC ii)angle DAC​

Answer 1

Answer:

ABC= 55°

DAC=20°

Step-by-step explanation:

hope it helps

Answer 2

Given:

DC parallel to AB.

∠CAB = 35°

To Find: ∠ADC and ∠DAC

Calculation:

In the circle from figure, angle subtended by AB on the circumference of circle ∠ACB is a central angle and is equal to $\frac{180}{2}$ = 90°.

Since AB || CD, so ∠DCA = ∠CAB = 35° by alternate angle theorem.

Now in ΔACB:

∠A + ∠B + ∠C = 180°

35° + ∠B + 90° = 180°

∠B = 55°

Since AB || CD,

∠CDA + ∠DAB = 180°

x + y = 145°

From quadrilateral ABCD:

∠D = 180° - ∠B = 180° - 55° = 125°

x = 125°

y = 145° - 125° = 20°

Answer:

∠ADC = 125°

∠DAC = 20°

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