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murzikaleks [220]
3 years ago
7

In rhombus MOTH, angle HTM=(5x+6) degrees. If angle HMO=(12x-6)degrees, what is angle HMO?

Mathematics
1 answer:
forsale [732]3 years ago
5 0

Answer:

m∠HMO=102°

Step-by-step explanation:

we know that

In a Rhombus the diagonals bisect the angles and opposite angles are equal

In this problem

Angles HMO and HTO are opposite angles

m∠HMO=m∠HTO

m∠HTM=(1/2)m∠HMO ----> because the diagonals bisect the angles and opposite angles are congruent

substitute the values

(5x+6)\°=(1/2)(12x-6)\°

solve for x

10x+12=12x-6\\12x-10x=12+6\\2x=18\\x=9

<em>Find the measure of angle HMO</em>

m∠HMO=(12x-6)°

substitute the value of x

m∠HMO=(12(9)-6)=102°

see the attached figure to better understand the problem

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