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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