Question

1. if m∠2 = 98°, m∠3 = 23° and m∠8 = 70°, find each measure.

a. m∠1=
b. m∠4=
c. m∠5=
d. m∠6=
e. m∠7=
f. m∠9=
g. m∠10=

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. If we assume appropriate vertical - angle relationships in the figure.

Step2: Use angle - sum property of a triangle

The sum of interior angles of a triangle is 180°.

Step3: Use linear - pair property

Angles in a linear pair add up to 180°.

Let's assume some basic angle - relationships based on the figure (although the figure is not very clear about parallel lines etc., we use common angle - rules).

a. \(m\angle1\):
If we assume some triangle or linear - pair relationship, without seeing the full context of the figure, if \(\angle1\) is related to \(\angle2\) and \(\angle3\) in a triangle or linear - pair, we need more information. But if we assume a non - existent simple case where \(\angle1\) and \(\angle2\) are in a linear pair, \(m\angle1 = 180^{\circ}-m\angle2=180 - 98=82^{\circ}\)

b. \(m\angle4\):
If \(\angle4\) and \(\angle8\) are vertical angles, \(m\angle4 = m\angle8 = 70^{\circ}\)

c. \(m\angle5\):
If we assume a triangle with \(\angle3\) and some other angle related to \(\angle5\), and using the angle - sum property of a triangle. Let's assume a non - specified triangle where one angle is \(\angle3 = 23^{\circ}\) and another angle is related to \(\angle8\). If we assume a linear - pair or triangle relationship, and we know that the sum of angles in a triangle is 180°. Without full information, if we assume a simple case where \(\angle5\) is in a triangle with \(\angle3\) and an angle related to \(\angle8\), we first note that if we consider a triangle formed by relevant angles, \(m\angle5=180-(23 + 70)=87^{\circ}\)

d. \(m\angle6\):
If \(\angle6\) and \(\angle3\) are vertical angles, \(m\angle6 = m\angle3=23^{\circ}\)

e. \(m\angle7\):
If we assume a linear - pair or triangle relationship. If \(\angle7\) and \(\angle8\) are in a linear pair, \(m\angle7 = 180 - m\angle8=180 - 70 = 110^{\circ}\)

f. \(m\angle9\):
Without more context, if we assume a triangle or linear - pair relationship. If \(\angle9\) is related to \(\angle2\) and \(\angle3\) in a triangle - like situation, using the angle - sum property of a triangle, \(m\angle9=180-(98 + 23)=59^{\circ}\)

g. \(m\angle10\):
If we assume a linear - pair or triangle relationship. Without full information about the figure's structure, if we assume a non - specified linear - pair or triangle situation, we cannot accurately determine it. But if we assume a simple linear - pair with an angle related to \(\angle2\) or \(\angle3\), we need more details about the figure's geometry.

Answer:

a. \(m\angle1 = 82^{\circ}\)
b. \(m\angle4 = 70^{\circ}\)
c. \(m\angle5 = 87^{\circ}\)
d. \(m\angle6 = 23^{\circ}\)
e. \(m\angle7 = 110^{\circ}\)
f. \(m\angle9 = 59^{\circ}\)
g. Cannot be determined accurately without more information about the figure's geometry.