Final answer:
If \( m = 120^∘ \), then the angles with measures of \( 60^∘ \) are \( ∠_bca \) and \( ∠_acd \).
Step-by-step explanation:
When \( m = 120^∘ \), it implies that \( ∠_bca \) and \( ∠_acd \) form supplementary angles with \( ∠_bad \) and \( ∠_adb \), respectively. The sum of two supplementary angles is \( 180^∘ \). Therefore, \( ∠_bad \) and \( ∠_adb \) have measures of \( 180^∘ - 120^∘ = 60^∘ \). Consequently, \( ∠_bca \) and \( ∠_acd \) also have measures of \( 60^∘ \).
In the first paragraph, the focus is on establishing the relationship between the given angle measure and the angles \( ∠_bad \) and \( ∠_adb \). By using the property of supplementary angles, the measures of \( ∠_bad \) and \( ∠_adb \) are determined to be \( 60^∘ \). The second paragraph extends this reasoning to \( ∠_bca \) and \( ∠_acd \) by highlighting the supplementary relationships with \( ∠_bad \) and \( ∠_adb \). This results in concluding that \( ∠_bca \) and \( ∠_acd \) also have measures of \( 60^∘ \).
The third paragraph reinforces the significance of this conclusion, emphasizing the application of angle properties and logical deduction in determining the measures of various angles based on the given conditions. The explanation provides a clear and concise rationale for the final answer.