Given: LMNP is a square A, B midpoints of LM and PN Q ∈ AB m∠LPQ = 45° Find: m∠PQN
2 answers:
Since A and B are the midpoints of ML and NP, we can say that AB is parallel to MN and LP. In order to find ∠PQN, we can work with the triangles PQB and NQB. According to SAS (Side-Angle-Side) principle, these triangles are congruent. BQ is a common side for these triangles and NB=BP and the angle between those sides is 90°, i.e, ∠NBQ=∠PBQ=90°. After finding that these triangles are equal, we can say that ∠BNQ is 45°. From here, we easily find <span>∠PQN. It is 180 - (</span>∠QNP + ∠NPQ) = 180 - 90 = 90°
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Answer:
ft tall
Step-by-step explanation:
We must follow the indications:
Ryan is 4 1/2 ft. tall.
Ryan =
He is 3 in. taller than his sister Lizzie. to find how tall is Lizzie we need to substract 3 inches from the height of Ryan, but we can only substract the quantities if they are in the same units.
Thus we convert the 3 inches to feet, since we 1 feet = 12 inches:
so the height of lizzie:
we convert the first mixed number to fraction by multiplying 4 by 12 and adding the numerator 1:
the subtraction becomes:
Lizzie is 23/6 ft tall.
She is 3/4 of a foot taller than her sister Emma, thus we must substract 3/4 from the height of Lizzie to find the height of Emma:
Emma is ft tall.