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1.If SPN= 118 and MT 72, find SN. 2.If ZMPT 135 and SN 157, find MT.​

1If SPN 118 And MT 72 Find SN 2If ZMPT 135 And SN 157 Find MT class=

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KAntoineDoixviz

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[tex] \large\underline{\mathbb{ANSWER}:} [/tex]

[tex] \qquad \Large \:\: \rm 1) \; m\overset{\frown}{SN} = 164\degree [/tex]

[tex] \qquad \Large \:\: \rm 2) \; m\overset{\frown}{MT} = 113\degree [/tex]

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[tex] \large\underline{\mathbb{SOLUTION}:} [/tex]

Number 1:

The measure of an angle and its vertical is half the sum of the measures of its intercepted arcs.

  • [tex] m\angle SPN = \frac12 (m\overset{\frown}{MT} + m\overset{\frown}{SN}) [/tex]

Substitute the given to find the measure of arc SN.

  • [tex] 118\degree = \frac12 (72\degree + m\overset{\frown}{SN}) [/tex]

  • [tex] (2)118\degree = \frac12 (72\degree + m\overset{\frown}{SN})(2) [/tex]

  • [tex] 236\degree = 72\degree + m\overset{\frown}{SN} [/tex]

  • [tex] 236\degree - 72\degree = m\overset{\frown}{SN} [/tex]

  • [tex] 164\degree = m\overset{\frown}{SN} [/tex]

Therefore, the measure of arc SN is 164°

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Number 2:

The measure of an angle and its vertical is half the sum of the measures of its intercepted arcs.

  • [tex] m\angle MPT = \frac12 (m\overset{\frown}{SN} + m\overset{\frown}{MT}) [/tex]

Substitute the given to find the measure of arc MT.

  • [tex] 135\degree = \frac12 (157\degree + m\overset{\frown}{MT}) [/tex]

  • [tex] (2)135\degree = \frac12 (157\degree + m\overset{\frown}{MT})(2) [/tex]

  • [tex] 270\degree = 157\degree + m\overset{\frown}{MT} [/tex]

  • [tex] 270\degree - 157\degree = m\overset{\frown}{MT} [/tex]

  • [tex] 113\degree = m\overset{\frown}{MT} [/tex]

Therefore, the measure of arc MT is 113°

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