Question

in the given figure find the measure of angle x.

Answer 1

50 DEGREE
BY SIMILARITY THEOREM OF TRIANGLES
IS IT OKAY NOW

Answer 2

Answer:

50°

Step-by-step explanation:

In ΔPQR , PQ=4.2 cm , QR = 7 cm, PR = 3√3

In ΔXYZ , XY= 14 cm , YZ=8.4 cm  , XZ= 6√3 cm

Now ,

$\frac{PQ}{YZ} =\frac{4.2}{8.4} =\frac{1}{2}$

$\frac{QR}{XY} =\frac{7}{14}=\frac{1}{2}$

$\frac{PR}{XZ} =\frac{3√3}{6√3}=\frac{1}{2}$

Since $\frac{PQ}{YZ} =\frac{QR}{XY}=\frac{PR}{XZ}$

Thus  ΔPQR  and ΔZYX are similar by SSS property

In ΔPQR Find ∠R using angle sum property (sum of all angles = 180°)

⇒∠P+∠Q+∠R=180°

⇒60°+70°+∠R=180°

⇒130°+∠R=180°

⇒∠R=180°-130°

⇒∠R=50°

Now since   ΔPQR  and ΔZYX are similar

So, their corresponding angles will be equal

So.∠R=∠X=50°

Hence the measure of angle X is 50°