Question

1. ∠fmg and ∠hmk are straight angles 1. given
2. m∠fmg = 180° and m∠hmk = 180° 2. definition of straight angle
3. m∠fmk + m∠kmg = m∠fmg m∠hmf + m∠fmk = m∠hmk 3. angle addition postulate
4. 4. substitution property of equality
5. m∠fmk + m∠kmg = m∠hmf + m∠fmk 5. transitive property of equality
6. m∠fmk = m∠fmk 6. reflexive property of equality
7. 7. subtraction property of equality

Explanation:

Step1: Substitute values from step 2 into step 3

Since \(m\angle FMG = 180^{\circ}\) and \(m\angle HMK=180^{\circ}\), we get \(m\angle FMK + m\angle KMG=180^{\circ}\) and \(m\angle HMF + m\angle FMK = 180^{\circ}\)

Step2: Use subtraction property of equality

Subtract \(m\angle FMK\) from both sides of the equation \(m\angle FMK + m\angle KMG=m\angle HMF + m\angle FMK\). We get \(m\angle KMG=m\angle HMF\)

Answer:

\(m\angle KMG=m\angle HMF\)