In the figure, AM ⊥ BC and AN is the bisector of ∠BAC. If ∠B = 70° and ∠C = 35°, find ∠MAN.
In the ΔABC, AN is the angle bisector of ∠BAC.
... ∠BAN = ∠NAC ........ (i)
Also ∠A + ∠B + ∠C = 180°
⇒ ∠A + 70° + 35° = 180°
⇒ ∠BAN + ∠NAC + 105° = 180°
⇒ 2 ∠BAN = 180° - 105° = 75°
... Δ BAM = 37.5°
In Δ ABM, we have ∠B + Δ BAM +Δ AMB = 180°
... 70° +∠BAM + 90° = 180°
... ∠BAM = 20° ....... (ii)
Now ∠MAN = ∠BAN - ∠BAM = 37.5° - 20° = 17.5°
... ∠BAN = ∠NAC ........ (i)
Also ∠A + ∠B + ∠C = 180°
⇒ ∠A + 70° + 35° = 180°
⇒ ∠BAN + ∠NAC + 105° = 180°
⇒ 2 ∠BAN = 180° - 105° = 75°
... Δ BAM = 37.5°
In Δ ABM, we have ∠B + Δ BAM +Δ AMB = 180°
... 70° +∠BAM + 90° = 180°
... ∠BAM = 20° ....... (ii)
Now ∠MAN = ∠BAN - ∠BAM = 37.5° - 20° = 17.5°
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of a right angle. Prove that m || n.
of a right angle.
