angleABDand angle ACEis exterior angles of triangle ABC.if angle ABD=110and angleACE=150,then find angleA
Answers
Answer:
Measure of Angle A is 80°
Step-by-step explanation:
Given: Measure of exterior angle ABD = 110°
Measure of exterior angle ACE = 150°
To find: m∠A
Figure is attached below.
We know that Sum of all exterior angles of a polygon is equal to 360°
⇒ ∠CAF + ∠ACE + ∠ABD = 360°
∠CAF + 150° + 110° = 360°
∠CAF + 260° = 360°
∠CAF = 360° - 260°
∠CAF = 100°
Also, Pair of interior angle and corresponding exterior angle are supplementary.
⇒ Interior angle + exterior angle = 180°
∠CAF + ∠BAC = 180°
∠BAC + 100° = 180°
∠BAC = 180° - 100°
∠BAC = 80°
Therefore, Measure of Angle A is 80°
Answer:
angleABDand angle ACEis exterior angles of triangle ABC.if angle ABD=110and angleACE=150, then AngleA = 80°
Step-by-step explanation:
∠ABD = 110°
∠ABD = ∠A + ∠C
∠ACE = 150°
∠ACE = ∠A + ∠B
∠ABD + ∠ACE = 110° + 150° = 260°
∠ABD + ∠ACE = ∠A + ∠C + ∠A + ∠B = ∠A + ∠A + ∠B + ∠C
Equating both
∠A + ∠A + ∠B + ∠C = 260°
as we know that ∠A + ∠B + ∠C = 180° ( sum of angles of a triangle)
∠A + 180° = 260°
=> ∠A = 80°