Question

Parallelogram ABCD is shown. Parallelogram A B C D is divided into 4 triangles by A C and B D which intersect at point E. Angle C A D is 27 degrees, angle A B D is 71 degrees, and angle C B D is 45 degrees. What is m∠BAC? m∠BAC =

Answer 1

• 37°

Task :

• To work out m∠BAC

Solution :

In order to find m∠BAC, we will consider the fact that the sum of all the interior angles of a llgm measures 360° wherein the opposite angles & sides are equal .

Thus,

• m∠ABC = m∠ADC
• m∠BAD = m∠BCD

ATQ,

• m∠ABC = m∠ABD + m∠CBD
• m∠BAD= m∠CAD + m∠BAC

Hence,

• m∠ABC = 71° + 45° = 116°
• m∠BAC = m∠BAD - 27° ......(1)

Since the opposite angles of a llgm are equal , therefore

• 2(m∠ABC + m∠BAD) = 360°
• m∠ABC + m∠BAD = 180°
• 116° + m∠BAD = 180°
• m∠BAD = 180° - 116°
• m∠BAD = 64°

from eq (1),

• m∠BAC = m∠BAD - 27°
• m∠BAC = 64° - 27°
• m∠BAC = 37°

hence,m∠ BAC = 37° .

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