Question

Find the value of each variable 16-21​

Answer 1

16.
`x = 80^\circ`

17.
`x = 55, y =70, z = 55`

18.
`x =8, y =3`

19.
`r = 66^\circ`,
`t = 73^\circ`

20.
`y = 70^\circ, x = 55^\circ`

21.
`x =56^\circ, y = 62^\circ`

Explanation:

16. Side
`AB = AC`

So, the opposite angles of the triangle will also be equal.

`\angle B =\angle C = 50^\circ`

Using triangle sum property, angle of all the internal angles of a triangle is equal to
`180^\circ`.

`50+50+x = 180\\\Rightarrow x = \bold{80^\circ}`

17. Two sides are given as equal,
`x = z`

Angles on a straight line are always equal to
`180^\circ`.

So,

`x + 125 = 180\\\Rightarrow x = 55`

`z = 55`

Using triangle sum property, angle of all the internal angles of a triangle is equal to
`180^\circ`.

`55+55+y = 180\\\Rightarrow y = \bold{70^\circ}`

18. All the angles are given equal to each other, therefore all the sides of the triangle will also be equal to each other.

`4x+7 = 13y =39`

`13y = 39\\\Rightarrow y = 3`

`4x +7 = 39\\\Rightarrow 4x = 32\\\Rightarrow x = 8`

19. Two sides are given equal to each other, therefore angles opposite to them will be equal.

Using the triangle sum property in the left triangle:

`r + 57 + 57 = 180\\\Rightarrow r = 66^\circ`

Using the property that vertically opposite angles are equal and the triangle sum property in the right triangle.

`t+50+57 = 180 \\\Rightarrow t = 73^\circ`

20. All the sides are given equal to each other.

So, all the angles will be equal to
`60^\circ`.

`y - 10 = 60\\\Rightarrow y = 70^\circ`

`x+5=60\\\Rightarrow x = 55^\circ`

21. Angles on a straight line are always equal to
`180^\circ`.

Angles opposite to equal sides in a triangle are also equal.

`118 + y = 180\\\Rightarrow y = 62^\circ`

Using triangle sum property:

`x+2y = 180\\\Rightarrow x = 180 - 124 = \bold{56^\circ}`