Let x represent the smaller angle. Then the larger one is 20+4x. Since they are complementary, their sum is 90. (All measures are degrees.)
90 = x + (20+4x)
90 = 5x +20
70 = 5x
14 = x
The smaller angle is 14°.
The larger angle is 76°.
Given:
∠PRS and ∠VUW are supplementary.
To prove:
Line TV || Line QS
Solution:
Step 1: Given
∠PRS and ∠VUW are supplementary.
Step 2: By the definition of supplementary angles
![m\angle {PRS}+m\angle {VUW}=180^{\circ}](https://tex.z-dn.net/?f=m%5Cangle%20%7BPRS%7D%2Bm%5Cangle%20%7BVUW%7D%3D180%5E%7B%5Ccirc%7D)
Step 3: Angles forming a linear pair sum to 180°
![m\angle {PRS}+m\angle {SRU}=180^{\circ}](https://tex.z-dn.net/?f=m%5Cangle%20%7BPRS%7D%2Bm%5Cangle%20%7BSRU%7D%3D180%5E%7B%5Ccirc%7D)
Step 4: By transitive property of equality
step 2 = step 3
![m\angle {PRS}+m\angle {VUW}=m\angle {PRS}+m\angle {SRU}](https://tex.z-dn.net/?f=m%5Cangle%20%7BPRS%7D%2Bm%5Cangle%20%7BVUW%7D%3Dm%5Cangle%20%7BPRS%7D%2Bm%5Cangle%20%7BSRU%7D)
Step 5: By algebra cancel the common terms in both side.
![{m} \angle {VUW}={m} \angle{SRU}](https://tex.z-dn.net/?f=%7Bm%7D%20%5Cangle%20%7BVUW%7D%3D%7Bm%7D%20%5Cangle%7BSRU%7D)
Step 6: By converse of corresponding angles postulate
Line TV || Line QS
Hence proved.
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Step-by-step explanation: