Question

find the size of the unknown angles .​

Answer 1

Answer:

Step-by-step explanation:

69+90+x=180

159+x=180

x=180-159

x=21

21+y+60=180

81+y=180

y=180-81

y=99

x=21 and y=99

Answer 2

Answer:

Consider triangle ADC,

AD = CD

So, angle CAD = angle ACD

Then, angle ACD = x

Now consider triangle ABC,

angle ABC = 69°

angle BAC = x + x = 2x

angle ACB = angle ACD = x

So, as per Angle Sum Property of triangle,

ABC + BAC + ACB = 180°

→ 69° + 2x + x = 180°

→ 3x = 180° - 69°

→ x = 111/3°

→ x = 37°

Now again consider triangle ADC,

Using Angle Sum Property of triangle,

y + x + x = 180°

→ y + 2x = 180°

→ y + 2 × 37 = 180° [x = 37]

→ y = 180° - 74

→ y = 106°

Therefore required value of x and y are 37° and 106° respectively.

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