Question

1. in the diagram, m∠agc = 38°, m∠cgd = 71°, and m∠fgc = 147°. find each angle measure.

a. m∠agb b. m∠dgf
c. m∠agf d. m∠bgd

1. smp.1 dig deeper how many times between 12 a.m. and 12 p.m.

Explanation:

Step1: Analyze angle - addition relationships

We know that angles around a point add up to 360 degrees and we use the given angle measures to find the unknowns.

Step2: Find \(m\angle AGB\)

Since \(\angle AGC = 38^{\circ}\) and assuming \(\angle BGC = 0^{\circ}\) (not given otherwise and for the sake of finding \(\angle AGB\) relative to \(\angle AGC\)), \(m\angle AGB=m\angle AGC = 38^{\circ}\)

Step3: Find \(m\angle DGF\)

We know that \(m\angle FGC=147^{\circ}\) and \(m\angle CGD = 71^{\circ}\). Since \(\angle DGF+\angle CGD=\angle FGC\), then \(m\angle DGF=m\angle FGC - m\angle CGD\). So \(m\angle DGF=147^{\circ}-71^{\circ}=76^{\circ}\)

Step4: Find \(m\angle AGF\)

\(m\angle AGF=m\angle AGC + m\angle FGC\). Substituting the given values, \(m\angle AGF=38^{\circ}+147^{\circ}=185^{\circ}\)

Step5: Find \(m\angle BGD\)

\(m\angle BGD=m\angle BGC + m\angle CGD\). Since \(m\angle BGC = 0^{\circ}\) (not given otherwise) and \(m\angle CGD = 71^{\circ}\), \(m\angle BGD = 71^{\circ}\)

Answer:

a. \(m\angle AGB = 38^{\circ}\)
b. \(m\angle DGF = 76^{\circ}\)
c. \(m\angle AGF = 185^{\circ}\)
d. \(m\angle BGD = 71^{\circ}\)