○=> Correct option :
[tex]\color{hotpink}\bold{ (a) \: 130}[/tex]
○=> Steps to derive correct option :
Angle (p+7)° and angle (3p+1)° are a linear pair so their sum will be equal to 180°.
Which means :
[tex] =\tt 3p + 1 + p + 7 = 180[/tex]
Let us solve that equation to find the value of p and the two angles :
[tex] =\tt 3p + 1 + p + 7 = 180[/tex]
[tex] =\tt 3p + p + 1 + 7 = 180[/tex]
[tex] =\tt 4p + 8 = 180[/tex]
[tex] = \tt4p = 180 - 8[/tex]
[tex] = \tt4p = 172[/tex]
[tex] =\tt p = \frac{172}{4} [/tex]
[tex]\hookrightarrow \tt \color{plum}p = 43[/tex]
Thus, value of p = 43
Measure of angle (p+7)° :
[tex] =\tt 43 + 7[/tex]
[tex]\tt\color{plum}angle \: (p + 7)° =\tt 50°[/tex]
Measure of angle (3p+1)° :
[tex] =\tt 43 \times 3 + 1[/tex]
[tex] = \tt129 + 1[/tex]
[tex]\tt\color{plum}angle \: (3p + 1)° = 130°[/tex]
Thus, the measure of the larger angle = 130°
Therefore, the correct option is (a) 130
