Question

HELPP

Given: Diameter QG,

mFG=46°, mQE =58°

Find: m∠GQF and m∠GPF


i already know that m∠GPF is 52
idk what ∠GQF

Answer 1

m∠GQF=23°

Explanation:

This is equal to 23 degrees because you know that mFG is 46°. Now, you use a theorem similar to Peripheral ∠ Th. to get 23°

Answer 2

`m\angle GQF=23^(\circ)`

`m\angle GPF=52^(\circ)`

Explanation:

We have been given an image of a circle and we are asked find the measure of angle GQF and measure of angle GPF.

We know that the measure of an inscribed angle is half the measure of its intercepted arc. To find the measure of angle GQF we will divide the measure of its intercepted arc (FG) by 2.

`m\angle GQF=(1)/(2)* 46^(\circ)`

`m\angle GQF=23^(\circ)`

Therefore, the m∠GQF is 23 degrees.

We know that measure of angle formed by two intersecting secants inside a circle is half the sum of their intercepted arcs.

`m\angle GPF=(1)/(2)*(\text{Measure of arc FG+arc QE})`

`m\angle GPF=(1)/(2)*(46^(\circ)+58^(\circ))`

`m\angle GPF=(1)/(2)*(104^(\circ))`

`m\angle GPF=52^(\circ)`

Therefore, the m∠GPF is 52 degrees.