Question

find the the size of each lettered angle in the figure ( i ) Angle BAC =90°​

Answer 1

Step-by-step explanation:

In figure 1 y is 20 and x is 80.

In figure 2 x is 40 and y is 130.

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Answer 2

Answer:

(i) x = 110° ; y = 20°

(ii) x = 40° ; y = 130°

(i) angle 1 = 50° ...( given triangle is isosceles}

in isosceles triangle

angle 1 + 50° + angle 2 = 180°

=> angle 2 = 180-(50+50)

=> angle 2 = 100°

also 30+ y = 50° { exterior angle = sum of opposite interior angle}

=> y = 20°

also,

y+ angle 2 + x = 180.....{they are supplementary angles}

=> (20)+(50)+x = 180

=> x = 180-70

=> x = 110°

(ii) in ∆ADC

angle 4 + 40° + 90 = 180

=> angle 4 = 180-30

=> angle 4 = 50°

also, angle 4 & x are complementary angles

=> angle 4 + x = 90°

=> x = 90-50

=> x = 40°

now , in ∆ABC

y = (90°+40°)....{ exterior angle= sum of opposite interior angle}

=> y = 130°