Question

find the value of y°
find the value of z°
​

Answer 1

Given x°, y° and z° lie on the same straight line.

Hence, x° + y° + z° = 180° ...[Equation 1]

(a) If y° = x° + z°, find the value of y.

Using equation 1, x° + y° + z° = 180°.

➸ x° + z° = 180° - y°

Now, given that y° = x° + z°.

➸ y° = 180° - y°

➸ 2y° = 180°

➸ y° = 180/2

$\huge{\underline{\sf{\red{ y° = 90°}}}}$

(b) If x° = y° = z°, find the value of z.

As, all the three variables are equal to each other.

Hence, x° + x° + x° = 180°

[Using equation 1]

➸ 3x° = 180°

➸ x° = 180/3

➸ x° = 60°

Now, we know that x° = z°.

$\huge{\underline{\sf{\red{Hence\: z° = 60°.}}}}$

$\small{\underline{\sf{\blue{Note:}}}}$

• Angles forming a straight line have the sum of the angles as 180°. This is because angle formed by a straight line is 180°.

Answer 2

Answer:

a)y=90°

b)z=60°

Step-by-step explanation:

a) since x+y+z=180 & y=x+z, substitute to get y=180-y. So y=90. Then x+z=90. i.e. Angles x & z can be any complementary angles.

b) If all three angles are congruent, they must each be 60. So z=60°.