Question

x°, y° and z° are three angles lying on a straight line. (a) If y = x + z, find the value of y. (b) If x' = y = z, find the value of z.

Answer 1

(a)
`\( x + z = 90^\circ \)`

(b)
`\( x = y = z = 60^\circ \)`

Step-by-step explanation:

(a) If
`\( y = x + z \)`, we can use the fact that the sum of angles on a straight line is 180 degrees. In this case, the sum of
`\( x \), \( y \), and \( z \)` should be equal to 180 degrees. So, we can express this relationship as:

`\[ x + y + z = 180^\circ \]`

Now, substitute
`\( y = x + z \)` into the equation:

`\[ x + (x + z) + z = 180^\circ \]`

Combine like terms:

`\[ 2x + 2z = 180^\circ \]`

Divide both sides by 2:

`\[ x + z = 90^\circ \]`

So, if
`\( x \), \( y \)`, and
`\( z \)` are three angles lying on a straight line, and
`\( y = x + z \)`, then
`\( x + z = 90^\circ \)`.

(b) If
`\( x' = y = z \)`, it implies that all three angles are equal. Let's denote this common angle as
`\( a \)`. Therefore,
`\( x = a \), \( y = a \)`, and
`\( z = a \)`. Since the sum of angles on a straight line is 180 degrees, we can write the equation:

`\[ x + y + z = 180^\circ \]`

Substitute the values:

`\[ a + a + a = 180^\circ \]`

Combine like terms:

`\[ 3a = 180^\circ \]`

Divide both sides by 3:

`\[ a = 60^\circ \]`

So, each angle
`\( x \), \( y \)`, and
`\( z \)` is
`\( 60^\circ \)`.