Question

Find the measures of the labeled angles.

3x° = °
(Type a whole number.)
3x0
(76-x)°

Answer 1

3x = 57

Explanation:

opposite angles are equal and so

3x = 76-x,

so, 4x=76

and x= 19

3*19 = 57

Answer 2

`\sf 3x ^\circ = \boxed{\,\, \sf 57 \,\,}^\circ`

Explanation:

Vertical angles are pairs of opposite angles formed by intersecting lines. They are always congruent, meaning they have the same measure.

In this case,we’re given the relationship between two vertical angles:

`\sf 3x^\circ = (76 - x)^\circ`

Let's solve for
`\sf x`:

`\sf 3x = 76 - x`

Add x on both sides:

`\sf 3x+x = 76 - x+x`

`\sf 4x = 76`

Divide by 4:

`\sf ( 4x )/(4)= (76)/(4)`

`\sf x = 19`

Now, substitute
`\sf x = 19` back into the expression
`\sf 3x^\circ` to find the measure of the labeled angles:

`\sf 3x ^\circ = 3(19) = 57^\circ`

So, the measure of the labeled angles is
`\sf 57^\circ`.