Question

Look at the figure, . Find the m∠H .

106°


42°


36°


74°

Answer 1

`74°`

Explanation:

In a parallelogram, opposite angles are congruent, and diagonals form a linear pair; m∠J [106°] and m∠H form a linear pair, so set them equal to 180°:

180° = 106° + m∠H

-106° - 106°

______________

74° = m∠H

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Answer 2

Answer : The value of ∠H is 74°

Step-by-step explanation :

As we know that the opposite sides and opposite angles are equal in parallelogram.

That means,

Side MJ = Side FH

Side FM = Side HJ

∠MFH = ∠MJH

∠FHJ = ∠FMJ

As we are given that:

∠MJH = ∠MFH = 106°

Let ∠FHJ = ∠FMJ = x

As we know that the sum of interior angles of quadrilateral is equal to 360°.

∠MFH + ∠MJH + ∠FHJ + ∠FMJ = 360°

∠MFH + ∠MFH + ∠FHJ + ∠FHJ = 360°

2∠MFH + 2∠FHJ = 360°

2(∠MFH + ∠FHJ) = 360°

(∠MFH + ∠FHJ) = 180°

(106° + ∠FHJ) = 180°

∠FHJ = 180° - 106°

∠FHJ = 74°

Therefore, the value of ∠H is 74°