Question

For question 6 what is that value of x?

For question 7 find m

Answer 1

(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;

`\angle P+\angle Q+\angle R=180^(\circ)`

Substituting the values, we get;

`x+14+6x-12+3x+8=180`

`10x+10=180`

`10x=170`

`x=17`

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;

`\angle G+\angle H +\angle I=180`

Substituting the values, we get;

`4x+13+8x-5+2x+4=180`

`14x+12=180`

`14x=168`

`x=12`

Thus, the value of x is 12.

The measure of ∠G:

Substituting x = 12 in m∠G = (4x+13)°, we get;

`m\angle G=(4(12)+13)^(\circ)`

`m\angle G=(48+13)^(\circ)`

`m\angle G=61^(\circ)`

Thus, the measure of angle G is 61°