Question

find the value of y in the following figure

Answer 1

Answer:

a. y = 180-(45+55)

      = 180- 100

      = 80

b. 104= y+y

    104 =2y

      52  = y

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Answer 2

The value of y in figure a.) is  80°, and the value of y in figure b.) is 52°

Step-by-step explanation:

Given:

In figure a. & ΔABC, ∠A= y, ∠B= 45°, ∠C= 55°

In figure b. & ΔPQR, ∠RQP= y, ∠RPQ=y, exterior angle QRS= 104°

To find:

value of y in both the figures

Solution:

For figure a.)

In ΔABC,

∠A= y, ∠B= 45°, ∠C= 55°............(given)

∴ ∠A+∠B +∠C = 180°......(angle addition property)

∴ y + 45°+  55°= 180°

∴ y+ 100°= 180°

∴ y = 180°-100°

∴ y = 80°

∴ ∠A = 80°

Thus the value of y for figure a.) is 80°

For figure b.)

In ΔPQR, ∠QRS is an exterior angle of the triangle

∠RQP= y, ∠RPQ=y, exterior angle QRS= 104°......(given)

Now, ∠QRS= ∠P+∠Q....(exterior angle theorem)

∴ 104°= y +y

∴ 104°= 2y

∴ 2y = 104°

∴ y= 104/2

∴ y = 52°

∴ ∠P = ∠Q= 52°

Thus, the measure or value for y in figure b.) is 52°

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