Answer:
8. m∠CBA = 170°
9. m∠CBA = 150°
Step-by-step explanation:
8. m∠CBA = m∠CBH + m∠ABH
The shape formed by points BCJH is a parallelgram, meaning its angles add up to 360°. If m∠JCB = 100°, then m∠BHJ is also 100°. The sum of those two angles is 200°, meaning the sum of m∠CBH and m∠CJH is equal to 160°. Since BCJH is a parallelogram, m∠CBH and m∠CJH should be equal. Therefore, m∠CBH and m∠CJH are equal to 80°.
m∠CBH = 80°
Since m∠BHG = 90° (indicated by the right angle symbol), and AB and GH are parallel, m∠ABH must also be 90°.
m∠ABH = 90°
m∠CBA = m∠CBH + m∠ABH = 80° + 90° = 170°
9. m∠CBA = m∠CBH + m∠ABH
Same premise as question 8 but with different values.
If m∠JCB = 120°, then m∠BHJ is also 120°. The sum of those two angles is 240°, meaning the sum of m∠CBH and m∠CJH is equal to 120°. Since BCJH is a parallelogram, m∠CBH and m∠CJH should be equal. Therefore, m∠CBH and m∠CJH are equal to 60°.
m∠CBH = 60°
Since m∠BHG = 90° (indicated by the right angle symbol), and AB and GH are parallel, m∠ABH must also be 90°.
m∠ABH = 90°
m∠CBA = m∠CBH + m∠ABH = 60° + 90° = 150°
