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Help me pleas I’m stuck

Help Me Pleas Im Stuck class=

Sagot :

MrRoyal

The measures of the angles are

  • The measure of angle ∠JPK is 50°
  • The measure of angle ∠LPM is 84°
  • The measure of angle ∠NPM is 50°
  • The measure of angle ∠JPI is 84°
  • The measure of angle ∠HPI is 46°

How to determine the measure of the angles?

Angle JPK

The given parameters are:

∠KPL = 46°

∠NPH = 25°

∠MPN = ∠NPH

By vertical angle theorem, we have:

∠JPK = ∠MPH

Where

∠MPH = ∠MPN + ∠NPH

This gives

∠MPH = ∠NPH + ∠NPH

So, we have:

∠MPH = 25° + 25°

Evaluate

∠MPH = 50°

Recall that:

∠JPK = ∠MPH

So, we have:

∠JPK = 50°

Hence, the measure of angle ∠JPK is 50°

Angle LPM

The angle on a straight line is 180°.

So, we have:

∠LPM +  ∠KPL + ∠MPH = 180°

This gives

∠LPM +  46° + 50° = 180°

Evaluate

∠LPM = 84°

Hence, the measure of angle ∠LPM is 84°

Angle NPM

In (a), we have:

∠NPM = ∠NPH

This gives

∠NPM = 50°

Hence, the measure of angle ∠NPM is 50°

Angle JPI

By vertical angle theorem, we have:

∠JPI = ∠LPM

So, we have:

∠JPI = 84°

Hence, the measure of angle ∠JPI is 84°

Angle HPI

By vertical angle theorem, we have:

∠HPI = ∠KPK

So, we have:

∠HPI = 46°

Hence, the measure of angle ∠HPI is 46°

Read more about vertical angles at:

https://brainly.com/question/24839702

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