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likoan [24]
3 years ago
10

What is the measure of angle c? (Brainliest and Bonus points for best answer)

Mathematics
2 answers:
k0ka [10]3 years ago
3 0

Answer:

\displaystyle 65°

Step-by-step explanation:

Angle <em>b</em> and 135° form a <em>linear pair</em>, so when summing them up to 180°, you will have 45° left over:

\displaystyle 180° = 135° + m∠b; 45° = m∠b

Now, by the <em>Vertical</em><em> </em><em>Angles</em><em> </em><em>Theorem</em>, angle <em>a</em> and 70°, in this case, are to be in <u>congruence</u> with each other, so you have that.

Now you must find the the measure of angle <em>c</em> sinse you have already found the measure of two angles already:

\displaystyle 180° = 45° + m∠c + 70° → 180° = 115° + m∠c; 65° = m∠c

I am joyous to assist you at any time.

Natali [406]3 years ago
3 0

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:

180=135+b

45=b

<u>Therefore, m∠b = 45. </u>

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:

a=70

<u>Therefore, m∠a = 70°.</u>

We also know that the angles inside of a triangle always add up to 180°. That means that b+a+c=180. So we can set up the following equation:

45+70+c=180\\115+c=180\\c=65

<u><em>Therefore, m∠c = 65°.</em></u>

Have a terrificly amazing day!

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