Question

1. if (mangle2 = 98^{circ}), (mangle3=23^{circ}) and (mangle8 = 70^{circ}), find each measure.

a. (mangle1=)
b. (mangle4=)
c. (mangle5=)
d. (mangle6=)
e. (mangle7=)
f. (mangle9=)
g. (mangle10=)

Explanation:

Step1: Find m∠1

In a triangle, the sum of interior - angles is 180°. Consider the small triangle with ∠2, ∠3 and the third angle. Let the third angle be x. Then x = 180°-(m∠2 + m∠3)=180°-(98° + 23°)=59°. ∠1 and x are vertical angles, so m∠1 = 59°.

Step2: Find m∠6

∠6 and ∠8 are supplementary (linear - pair). So m∠6=180° - m∠8 = 180° - 70°=110°.

Step3: Find m∠7

Consider the triangle with ∠6, ∠7 and ∠3. Using the angle - sum property of a triangle, m∠7=180°-(m∠6 + m∠3)=180°-(110° + 23°)=47°.

Step4: Find m∠4

∠4 and ∠7 are vertical angles. So m∠4 = m∠7 = 47°.

Step5: Find m∠5

∠5 and ∠2 are vertical angles. So m∠5 = m∠2 = 98°.

Step6: Find m∠9

∠9 and ∠6 are vertical angles. So m∠9 = m∠6 = 110°.

Step7: Find m∠10

∠10 and ∠8 are vertical angles. So m∠10 = m∠8 = 70°.

Answer:

a. m∠1 = 59°
b. m∠4 = 47°
c. m∠5 = 98°
d. m∠6 = 110°
e. m∠7 = 47°
f. m∠9 = 110°
g. m∠10 = 70°