Hello and Good Morning/Afternoon:
Let's take this problem-step-by-step:
Let's consider the information given to us:
[tex]\hookrightarrow \text{one angle has a measure of 51 degrees}[/tex]
What does this problem want us to find:
[tex]\hookrightarrow \text{measure of angle b and c}[/tex]
Let's solve:
- Find the measure of angle b
⇒ By the vertical angle theorem --> ∠b = 51
- Find the measure of angle c
⇒ sum of all the angles in this picture is 360 degrees
⇒ b + c + 51 + c = 360
(there are two 'c' because the angle opposite c is equal to it)
[tex]b + c + 51 + c=360\\51 + 51 + 2c = 360\\102 + 2c = 360\\2c = 258\\c = 129[/tex]
Terminology used:
- Vertical Angle theorem: angles that are opposite to each other and are formed by two intersecting straight lines are congruent to each other
Answer:
Hope that helps!
#LearnwithBrainly
