Question

1. when an air hockey puck is hit into the sideboard, it bounces off so that ∠1 and ∠2 are congruent. m∠1 + m∠2 = 130°. find: m∠1 = __ m∠2 = m∠3 = m∠4 = __ 15. (overrightarrow{bd}) bisects ∠abc. find the value of x. 16. find the value of x bel

Explanation:

Step1: Find m∠1 and m∠2

Since ∠1 and ∠2 are congruent and m∠1 + m∠2 = 130°, let m∠1=m∠2 = x. Then x + x=130°, 2x = 130°, so $x=\frac{130^{\circ}}{2}=65^{\circ}$. Thus m∠1 = 65° and m∠2 = 65°.

Step2: Find m∠3

∠1 and ∠3 are supplementary (a straight - line is 180°). So m∠3=180° - m∠1. Substituting m∠1 = 65°, we get m∠3 = 180°-65° = 115°.

Step3: Find m∠4

∠2 and ∠4 are supplementary. So m∠4=180° - m∠2. Substituting m∠2 = 65°, we get m∠4 = 180° - 65°=115°.

Step4: Solve for x in problem 15

Since $\overrightarrow{BD}$ bisects ∠ABC, then m∠ABD=m∠DBC. So 10x - 51=6x - 11. Subtract 6x from both sides: 10x-6x - 51=6x-6x - 11, 4x - 51=-11. Add 51 to both sides: 4x-51 + 51=-11 + 51, 4x = 40. Divide both sides by 4: $x = 10$.

Answer:

m∠1 = 65°
m∠2 = 65°
m∠3 = 115°
m∠4 = 115°
x (in problem 15)=10