Answer:
a. 102° and 51°
b. ∠a = 142°, ∠c = 38°
Step-by-step explanation:
a. The sum of angles on a straight line equals
180°.
We can write an equation according to this:
[tex]27° + 2x° + x° = 180°[/tex]
Put terms with x to the left and numbers to the right (signs change into opposite ones when moving sides):
[tex]2x° + x° = 180° - 27°[/tex]
Collect like-terms:
[tex]3x° = 153°[/tex]
Divide both sides of the equation by 3:
[tex]x = 51°[/tex]
Therefore, the missing angles are:
2x° = 2 × 51° = 102°
and
x° = 51°
.
b. Vertically opposite angles are the same size.
Let's write an equation according to this:
[tex]a° = 142°[/tex]
The sum of angles around a point equals 360°.
Now we can find ∠c:
∠c= [tex] \frac{360° - 142° - 142°}{2} = 38°[/tex]
Therefore, ∠a = 142°, ∠c = 38°.
