Mathematics
In the following figure, AB = AC and AD = AE.
If ∠B = 50° ∠D = 66° and ∠GAC = 18°, find the measure of angles DAE, BAF and AGF.
Answer
Given, AB = AC and AD = AE.
In Δ ADE,
AD = AE
Hence, ∠ADE = ∠AED = 66° (Isosceles triangle property)
As we know that sum of all angles in triangle ADE = 180°.
⇒ ∠ADE + ∠AED + ∠DAE = 180°
⇒ 66° + 66° + ∠DAE = 180°
⇒ 132° + ∠DAE = 180°
⇒ ∠DAE = 180° - 132°
⇒ ∠DAE = 48°
In Δ ABC,
AB = AC
Hence, ∠ABC = ∠ACB = 50° (Isosceles triangle property)
As we know that sum of all angles in triangle ABC = 180°.
⇒ ∠ABC + ∠ACB + ∠BAC = 180°
⇒ 50° + 50° + ∠BAC = 180°
⇒ 100° + ∠BAC = 180°
⇒ ∠BAC = 180° - 100°
⇒ ∠BAC = 80°
As, ∠BAF + ∠FAG + ∠GAC = 80°
⇒ ∠BAF + 48° + 18° = 80°
⇒ ∠BAF + 66° = 80°
⇒ ∠BAF = 80° - 66°
⇒ ∠BAF = 14°
Now, using exterior angle property,
⇒ ∠AGF = ∠GAC + ∠GCA
= 18° + 50°
= 68°
Hence, the angles DAE = 48°, BAF = 14° and AGF = 68°.
Related Questions
Two sides AB and BC and median AD of triangle ABC are respectively equal to sides PQ and QR and median PN of △PQR. Show that :
(i) △ABD ≡ △PQN.
(ii) △ABC ≡ △PQR.
The given figure shows PQ = PR and ∠Q = ∠R
Prove that: △PQS ≡ △PRT.
In △ABC, AB = BC, AD ⊥ BC and CE ⊥ AB. Prove that AD = CE.
Use the informations given in the following figure to find the values of x and y.
