Question

four angles share a vertex. m<1=98,m<2=82,m<3=93

Answer 1

To find the measure of the fourth angle, we can use the fact that the sum of the measures of the interior angles of a quadrilateral is always 360 degrees.

Let's denote the measure of the fourth angle as m<4.

Sum of the measures of the angles: m<1 + m<2 + m<3 + m<4 = 360

Substituting the given measures of angles:

98 + 82 + 93 + m<4 = 360

273 + m<4 = 360

Subtracting 273 from both sides:

m<4 = 360 - 273

m<4 = 87

Therefore, the measure of the fourth angle is 87 degrees.