Answer:
[tex]\displaystyle 65°[/tex]
Step-by-step explanation:
Angle b and 135° form a linear pair, so when summing them up to 180°, you will have 45° left over:
[tex]\displaystyle 180° = 135° + m∠b; 45° = m∠b[/tex]
Now, by the Vertical Angles Theorem, angle a and 70°, in this case, are to be in congruence with each other, so you have that.
Now you must find the the measure of angle c sinse you have already found the measure of two angles already:
[tex]\displaystyle 180° = 45° + m∠c + 70° → 180° = 115° + m∠c; 65° = m∠c[/tex]
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Hey there!
The answer to your question is 65°.
To solve for m∠c, we first need to solve for m∠a and m∠b.
First, we will solve for m∠b:
We can see that ∠b is right next to the angle that measures 135°. Those two angles are supplementary angles, and form a linear pair. Therefore, their angle sum is 180°. (This is the linear pair postulate) So we can set up the following equation:
[tex]180=135+b[/tex]
[tex]45=b[/tex]
Therefore, m∠b = 45.
Now, we have to solve for m∠a. Using the vertical angles theorem, we know that if two lines intersect, the angles vertical of eachother are always equal. ∠a and the angle that measures 70° are vertical angles, and congruent. So:
[tex]a=70[/tex]
Therefore, m∠a = 70°.
We also know that the angles inside of a triangle always add up to 180°. That means that [tex]b+a+c=180[/tex]. So we can set up the following equation:
[tex]45+70+c=180\\115+c=180\\c=65[/tex]
Therefore, m∠c = 65°.
Have a terrificly amazing day!