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Step2247 [10]
2 years ago
15

I need help to answer please

Mathematics
1 answer:
WARRIOR [948]2 years ago
6 0

Answer:

m∠N = 41°

Step-by-step explanation:

Here,

In △MNO, m∠M = (6x + 1°) ...(1)

m∠N = (3x - 10°) ...(2)

m∠0 = (x + 19°) ...(3)

Here, We know that the sum of all angles of a triangle is 180°

Then,

(6x + 1°) + (3x - 10°) + (x + 19°) = 180°

6x + 1° + 3x - 10° + x + 19° = 180°

6x + 3x + x + 1° - 10° + 19° = 180°

10x + 10° = 180°

10x = 180° - 10°

10x = 170°

x = 170° ÷ 10°

x = 17°

Now, put the value of x in (1), (2) and (3)

m∠M = (6x + 1°)

= (6(17) + 1°)

= (102° + 1°)

<u>m∠M = 103°</u>

m∠N = (3x - 10°)

= (3(17) - 10°)

= (51° - 10°)

<u>m∠N = 41°</u>

m∠0 = (x + 19°)

= (17 + 19°)

<u>m∠0 = 36°</u>

Thus, The m∠N = 41°

<h3><em><u>F</u></em><em><u>O</u></em><em><u>R</u></em><em><u> </u></em><em><u>V</u></em><em><u>E</u></em><em><u>R</u></em><em><u>I</u></em><em><u>F</u></em><em><u>I</u></em><em><u>C</u></em><em><u>A</u></em><em><u>T</u></em><em><u>I</u></em><em><u>O</u></em><em><u>N</u></em><em><u> </u></em><em><u>O</u></em><em><u>N</u></em><em><u>L</u></em><em><u>Y</u></em><em><u>:</u></em></h3>

(6x + 1°) + (3x - 10°) + (x + 19°) = 180°

(6(17) + 1°) + (3(17) - 10°) + (17 + 19°) = 180°

103° + 41° + 36° = 180°

180° = 180°

Hence, L.H.S = R.H.S

<u>-</u><u>T</u><u>h</u><u>e</u><u>U</u><u>n</u><u>k</u><u>n</u><u>o</u><u>w</u><u>n</u><u>S</u><u>c</u><u>i</u><u>e</u><u>n</u><u>t</u><u>i</u><u>s</u><u>t</u>

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