Find the values of x and y using the information shown in the given fi

1.	Find the values of x and y using the information shown in the given figure. Find the measures of ∠ABD and ∠ACD
Answer» i. ∠ACB = 50° [Given] In ∆ABC, seg AC ≅ seg AB [Given] ∴ ∠ABC ≅ ∠ACB [Isosceles triangle theorem] ∴ x = 50° ii. ∠DBC = 60° [Given] In ABDC, seg BD ≅ seg DC [Given] ∴ ∠DCB ≅ ∠DBC [Isosceles triangle theorem] ∴ y = 60° iii. ∠ABD = ∠ABC + ∠DBC [Angle addition property] = 50° + 60° ∴ ∠ABD = 110° iv. ∠ACD = ∠ACB + ∠DCB [Angle addition property] = 50° + 60° ∴ ∠ACD = 110° ∴ x = 50°, y = 60°, ∠ABD = 110°, ∠ACD = 110°

Find the values of x and y using the information shown in the given figure. Find the measures of ∠ABD and ∠ACD

Answer»

i. ∠ACB = 50° [Given]

In ∆ABC, seg AC ≅ seg AB [Given]

∴ ∠ABC ≅ ∠ACB [Isosceles triangle theorem]

∴ x = 50°

ii. ∠DBC = 60° [Given]

In ABDC, seg BD ≅ seg DC [Given]

∴ ∠DCB ≅ ∠DBC [Isosceles triangle theorem]

∴ y = 60°

iii. ∠ABD = ∠ABC + ∠DBC [Angle addition property]

= 50° + 60°

∴ ∠ABD = 110°

iv. ∠ACD = ∠ACB + ∠DCB [Angle addition property]

= 50° + 60°

∴ ∠ACD = 110°

∴ x = 50°, y = 60°,

∠ABD = 110°, ∠ACD = 110°