Answer:
The angles of the triangle from smallest to largest are ∠X, ∠Y, ∠Z and sides are YZ, XZ, XY. So the option B is correct.
Step-by-step explanation:
From the given figure ∠Z is right angle therefore ΔXYZ is Right angle triangle.
Here we have to given that
∠X = ( 2 X + 1)°........................(i)
∠Y = ( 2 X + 9)°........................(ii)
∠ Z = 90° ................................(iii)
As we know that-
" The sum of three angles of any triangle is 180°. "
i.e. ∠X + ∠Y + ∠Z = 180°................................(iv)
Now putting all values of equation (i), (ii), (iii) in equation (iv)-
( 2 X + 1 )° + ( 2 X + 9 )° + 90° = 180°
4 X + 100° = 180°
4 X = 180° - 100°
4 X = 80°
X = 20°
Now putting X = 20° in equation (i), (ii), (iii)-
∠ X = 2× 20° + 1 = 41°
∠ Y = 2× 20° + 9 = 49°
∠ Z = 90°
Hence the angles from smallest to largest are ∠ X , ∠Y and ∠ Z.
As the given triangle is Right Angle Triangle therefore by the Pythagorean theorem
X Y is the hypotenuse,Y Z is base and X Z is height.
Hence the sides from smallest to largest are Y Z, X Z and X Y.
