Question

if ∠5 and ∠7 are supplementary and m∠5 = 55°. find the measures of the remaining numbered angles. m∠4 = m∠6 =

Explanation:

Step1: Find measure of ∠7

Since ∠5 and ∠7 are supplementary, and supplementary angles add up to 180°. Given m∠5 = 55°, then m∠7=180° - 55° = 125°.

Step2: Find measure of ∠4

∠4 and ∠5 are a linear - pair (adjacent and supplementary). So m∠4 = 180° - m∠5. Substituting m∠5 = 55°, we get m∠4 = 125°.

Step3: Find measure of ∠6

∠5 and ∠6 are vertical angles. Vertical angles are equal. So m∠6=m∠5 = 55°.

Step4: Find measure of ∠8

∠7 and ∠8 are vertical angles. Vertical angles are equal. So m∠8=m∠7 = 125°.

Answer:

m∠4 = 125°
m∠6 = 55°
m∠7 = 125°
m∠8 = 125°