Answer :
The measures of the three remaining angles are:
[tex]\angle ZQ = 64$^{\circ}$\\\angle ZR = 116$^{\circ}$\\\angle ZS = 64$^{\circ}$[/tex]
Given the information provided:
Angle [tex]\angle SPR[/tex] measures 116°.
In a triangle, the sum of all angles is 180°.
To find the measures of the three remaining angles [tex]\angle ZQ, \angle ZR, \angle ZS[/tex], we can use the fact that the sum of all angles in a triangle is 180°.
1. Find the measure of angle [tex]\angle ZQ[/tex] :
The sum of angles [tex]\angle SPR and \angle ZQ[/tex] should be 180°.
[tex]\angle ZQ = 180$^{\circ}$ - \angle SPR = 180$^{\circ}$ - 116$^{\circ}$ = 64$^{\circ}$[/tex]
2. Find the measure of angle [tex]\angle ZR[/tex] :
The sum of angles [tex]\angle ZQ and \angle ZR[/tex] should be 180°.
[tex]\angle ZR = 180$^{\circ}$ - \angle ZQ = 180$^{\circ}$ - 64$^{\circ}$= 116$^{\circ}$[/tex]
3. Find the measure of angle [tex]\angle ZS[/tex] :
The sum of angles [tex]\angle ZR and \angle ZS[/tex] should be 180°.
[tex]\angle ZS = 180$^{\circ}$ - \angle ZR = 180$^{\circ}$ - 116$^{\circ}$ = 64$^{\circ}$[/tex]
Therefore, the measures of the three remaining angles are:
[tex]\angle ZQ = 64$^{\circ}$\\\angle ZR = 116$^{\circ}$\\\angle ZS = 64$^{\circ}$[/tex]
So, the correct answer is:
[tex]\angle ZQ = 64$^{\circ}$ , \angle ZR = 116$^{\circ}$ , \angle ZS = 64$^{\circ}$ .[/tex]
Question :
The measures of the three remaining angles are: Measure of angle Q = 64 degrees, Measure of angle R = 116 degrees,
and Measure of angle S = 64 degrees.
In a parallelogram, opposite angles are equal, and the sum of the interior angles is 360 degrees. Given angle P is 116 degrees, and angle R is opposite to angle P, angle R must also be 116 degrees. Since we know two opposite angles, we can find the measure of the other two angles (Q and S) by subtracting the sum of angles P and R from 360 degrees.
So, we calculate:
Sum of angles P and R: 116 degrees + 116 degrees = 232 degrees
Remaining degrees for angles Q and S in the parallelogram: 360 degrees - 232 degrees = 128 degrees
Since angles Q and S are also opposite each other, they will be equal, and therefore each will be half of 128 degrees: 128 degrees / 2 = 64 degrees.
Hence, the measures of the three remaining angles are:
Measure of angle Q = 64 degrees,
Measure of angle R = 116 degrees,
Measure of angle S = 64 degrees.
