(6) Given that in ΔPQR, m∠P = (x+14)°, m∠Q = (6x-12)° and m∠R = (3x+8)°
We need to determine the value of x.
Value of x:
By triangle sum property, we have;
[tex]\angle P+\angle Q+\angle R=180^{\circ}[/tex]
Substituting the values, we get;
[tex]x+14+6x-12+3x+8=180[/tex]
[tex]10x+10=180[/tex]
[tex]10x=170[/tex]
[tex]x=17[/tex]
Thus, the value of x is 17
(7) Given that ΔGHI, m∠G = (4x+13)°, m∠H = (8x-52)° and m∠I = (2x+4)°
We need to determine the measure of ∠G
Value of x:
By triangle sum property, we have;
[tex]\angle G+\angle H +\angle I=180[/tex]
Substituting the values, we get;
[tex]4x+13+8x-5+2x+4=180[/tex]
[tex]14x+12=180[/tex]
[tex]14x=168[/tex]
[tex]x=12[/tex]
Thus, the value of x is 12.
The measure of ∠G:
Substituting x = 12 in m∠G = (4x+13)°, we get;
[tex]m\angle G=(4(12)+13)^{\circ}[/tex]
[tex]m\angle G=(48+13)^{\circ}[/tex]
[tex]m\angle G=61^{\circ}[/tex]
Thus, the measure of angle G is 61°
