Question

In Figure-4, A ABC and A XYZ are shown. If AB = 3.8 cm, AC = 3/3 cm,
BC = 6 cm, XY = 6/3 cm, XZ = 7.6 cm, YZ = 12 cm and ZA = 65°,
B = 70°, then find the value of Z Y.
/65
3 13 cm
3.8 cm
6√3 cm/
7.6 cm
70°
B
6 cm
Y
12 cm
Z​

Answer 1

Answer:

Step-by-step explanation:

abc is similar pqr

hece

angle x=65

angle y=70

we know that sum of interior angles=180 in triangle

x+y+z=180

65+70+z=180

135+z=180

z=45

hence value of z and y are 45 and 70 degree

Answer 2

The value of ∠Y is 45°

Given,

Two triangles ΔABC and ΔXYZ

AB = 3.8 cm,

AC = 3√3 cm,

BC = 6 cm, XY = 6√3 cm, XZ = 7.6 cm, YZ = 12 cm and ∠A = 65°, ∠B = 70°

To find,

The value of ∠Y

Solution,

Draw the given two triangles ΔABC and ΔXYZ

and assign the measurements AB = 3.8 cm, AC = 3√3 cm,

BC = 6 cm, XY = 6√3 cm, XZ = 7.6 cm, YZ = 12 cm and ∠A = 65°, ∠B = 70°

In ΔABC and ΔXYZ,

AB/XZ = 3.8/7.6

so, AB/XZ = 1/2

BC/YZ = 6/12

so, BC/YZ = 1/2

AC/XZ = 3√3/6√3

so, AC/XZ = 1/2

By, Side-Side-Side property of triangles,

∠X = ∠A = 65°

∠Z = ∠B = 70°

Now, let's use the angle sum property of the triangle,

In ΔXYZ,

∠X + ∠Y + ∠Z = 180°

65° + ∠Y + 70° = 180°

∠Y + 135° = 180°

∠Y = 45°

Hence, The value of ∠Y is 45°

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