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3 years ago

If the m∠SRW = 85°, what are the measures of ∠VRU and ∠URW?

Mathematics

2 answers:

Lady bird [3.3K]3 years ago

7 0

Answer:

∠VRU = 80°

∠URW = 15°

Step-by-step explanation:

Given that,

∠TRV = ∠SRW ( vertical opposite angle)

2x + 15 = 85

2x = 70

x = 35

So,

∠VRU = 2x + 10

∠VRU = (2×35) + 10

∠VRU = 70 + 10

∠VRU = 80°

∠URW = 180 - ∠VRU - ∠SRW

∠URW = 180 - 85 - 80

∠URW = 15°

netineya [11]3 years ago

6 0

Answer:

80 and 15

Step-by-step explanation:

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In the pulley system shown in this figure, MQ = 30 mm, NP = 10 mm, and QP = 21 mm. Find MN.

ankoles [38]

<h2>Answer:</h2>

$\boxed{\overline{MN}=37.96}$

<h2>Step-by-step explanation:</h2>

For a better understanding of this problem, see the figure below. Our goal is to find $\overline{MN}$ . Since:

$\angle MRS=\angle MQP=90^{\circ} \\ \\ \overline{MQ}=\overline{MR}=30mm$

and $\overline{MN}$ is a common side both for ΔMRN and ΔMQN, then by SAS postulate, these two triangles are congruent and:

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$\overline{QN}=\sqrt{\overline{NP}^2+\overline{QP}^2} \\ \\ \overline{QN}=\sqrt{10^2+21^2} \\ \\ \overline{QN}=\sqrt{541}$

Applying Pythagorean theorem again, but for triangle MQN:

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