Answer:
96°
Step-by-step explanation:
The given quadrilateral is inscribed in a circle, so its opposite angles are supplementary, which means that the sum of their measures is 180∘.
The measures of the opposite angles in the quadrilateral are given as (6m + 1 3)∘ and (4m + 7)∘.
Equate the sum of the given measures to 180∘.
6m + 13 + 4m + 7 = 180
Combine like terms.
10m + 20 = 180
Subtract 20 from both sides.
10m = 160
Divide both sides by 10.
m = 16
Substitute 16 for m into the expression given for the measure of angle M and simplify.
6m = 6(16)
=96∘
Therefore, m∠M = 96∘.
