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Q.

In a triangle ABC, what is https://lh3.googleusercontent.com/nitxv1nOmqdIDgiboO5jmggJ631EEcfkGiIQUyIN93aYtZsSG5mSFnmEwkusbXXUhKBjvtp3ITPO-5LgDSRzfVQayKLfvNwlNkhiRL_k7CowgmGhUFamwjpAaWsijK9DAuHw8JAab4HBNuyjWdPPYw, given https://lh6.googleusercontent.com/N1T6OMry_tC9mv6WKuNCpP8UeUrxe4UeJ9g1JYnx3E3w_tYlF3PljK5jUJ_HJ8K_ySmy2OXD8l07dnFZr5vY0m4bbZz1mP2_7FzNHpb7tO_Z9a1WY_e6lUm32Y5bRBhBCB_X_3wMgiSHM9yPR4bKDQhttps://lh4.googleusercontent.com/OFLnvTK54kJiR95d5L7h_mk-R2b-K1saCjFwBs_2UBmWlJ5ItmWsU6HZHwMuIrCD2rVzxfzH8dqdLTTQMftqL6k_7u8-x3HfFX5ihQ85Rhq-RuHw2eAipOhM1fhbdKKdgh-Dx-mTqReGVLE6PCnskg


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a

https://lh4.googleusercontent.com/AaNv_y-EdATdGnQlXRfetMUyMOt8JWSdzsfHkPoSGMR3873JG8rxmPd76i51yGg51icltL3GRkJx-eFA6WWouN1yDmX_45Ygae2_vejV99b4LHWxnYSaa84XPRMCPKMRaprF2k25LW5zo2DTkvhdEA

b

https://lh6.googleusercontent.com/FvMBWPYpcL4bi8qrQrDdxYOQEBsxwpm7v8pS7-FFLB2N1F0u7MqWul1bmUvdSpueUK3JSKBy-Y6fo--raIEiSNQkUXAH7Qy2e6y4vhSy3mgRKLO6BSFNA6F2uTtF4eo_tXF88dtJMQZRjLPx9e4LVg

c

https://lh5.googleusercontent.com/12y1_pYBP8C2Nyl1kbXV3JLe14QUEzDT8ddnfFxRj-T9xB6AuuvegjNmld0Kmvb_fxqmZWR-V5D3Tpzj-Gf0T6U5dBA1EaYdiuCVoLdAYY2UQh1RosbshXMnbLk5OPwuQs-d3g5WzVVeBRb6khgxgg

d

https://lh3.googleusercontent.com/wq_sJYqhJyFkFawlUBfwoF5V4lC3-UU5U-K9mj361adC0cb-rKHqSgLcgRZgRNGEh3vMw52XXr0FlqW5_5FPBefHjv3iYnzs04ifBPvMEaEuwcDE_rBcwSCuPVvewm48nmkkuSooezh9bz0yZ-sSUw 

answer is C.

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Detailed Solution

Concept: By utilizing the fact that angles on the same line add to https://lh3.googleusercontent.com/yamCFVEv3hHdIcDAV6CFdKo1IdRnmtbNSZHF2dOfVCU0ByOm0V-E_eXpD7GigVsT7CueJOvl5MS23cDXO8XOQVJhxrnuWKaALksajY-s5yCfME8vwaS6U51QgB67rzOn4RVSSIfOFokWW2zc6AZ50Q, we will first determine the value of ACB. The angle sum property will then be applied to the triangle ABC, giving us the result https://lh4.googleusercontent.com/cHMryA66sGL4C8JtLkStYGUPu3u7PJFdj1XaAH3WlbGafABh3XlUdIcbjX55UnmV0J1Ld4aQE4jzcNi1pTAGPY8HGlDF7dh5prrPnU-UbmziSv19tkJMKcAZnMLeugdlEibZNFdJDd3yQ-VIy-CL7g. Find the value of A after substituting the known values.
We have the value of https://lh6.googleusercontent.com/bKYxHV70WE58QoBpg5g9jy7OsQEq498JvYyRFyPk9OmgxvI8HdKBQ7HrCv-s0eevTbA-BONSutuTZgPlxL4ORGhdQUFwHhfGmQx4_Im1siap79ieTX38HJ2Y3sPlWn4KwIs_VEuEw85-ZbpjIf4UcA and https://lh5.googleusercontent.com/B3eoa1HUegWB77AueDjpOfwYlLXuYnud_H_hNLyBJPeSgKcVm-P-v3YegoJUZ0oMTT8ONlagUYKHcee3-8puBA9D_6o2TfSluoS1a0DVNiyWSU4IDkOvGD8v5th0BAx1nWs-WSbqFTxfJxvxTN-4VwWe have to find the value of https://lh5.googleusercontent.com/4PNlTGbIRO0l0aU6MELJlSiqfU_7h4wyZU3aeCIqy6nLb2il7H6sswcLNSfjYybauNrcgyU9en6eGN47WTjo2NQ3rM-BzA0GFstHRMJ8JJ-Rdzt1MPXNwyZfJWqOGsQUR_IjNPXUzYVcYWik2SE0RgFirst , we will find the value of https://lh5.googleusercontent.com/GUNmOXCShrG_zTOxbnGEZaJ4gpk48j6IEz-BzzJffXIYnU6QSa9LGByVvN_btW4brVpw3teEMSHcL81bJ25gOWXmhiwBY3dVEUFr5ufA20dxdjnBj3LiIc9g8FRPHws_kDJq3rB2-2apby6elfsI-AWe can see that the angles https://lh3.googleusercontent.com/yWGU1so5g78Se1gmzDhaFZiIKnER6tHuYOOr005y4PIYcoS7ciZj4omV317dMXZ7pUBc7gU1-ujgfqfCDsXZOrA_ZJsgFXVS68-8wtuuhd_gFszTWBYA1EtH0fCIBBqYnslcxiV4o6COTOWAoSht9g are on same line, thus the sum of these angles is https://lh5.googleusercontent.com/KKiAePsqrT_B0Q8T45Zr0MzRVuPumK0qT0PizAQoQPvej-Id6llnBq10I5j1-Wgt-wMkNYuPnHz8d7NsoWbbZz4y6xWbjBhaJzmyTIm6tEzIPlKb2HqBwoO_4u-9fB7DIc5-1ziYadJcRk72qzuwJwhttps://lh6.googleusercontent.com/J8XWFs8JlrBrhnqqIjpCIjx5qIqgKb4J30RmCXqzFFo7SdfNAi89kwodBtcZI2CKM0FaYx_ltO7usEO2btqtqCdvKpYE_-b7IjUy_cZOXW4nGhZBhgK56zB2GdopWizkyi_fvtWaNt5xXVHrE915HAWe will now replace the value of https://lh3.googleusercontent.com/fEtFzRwtFkHJpBQ9sJ80RG7ssAk0fP1SE2bMAhkyLhYNHMzcHGHKdYHg6eIonnnm8Cwe77mjLbRJ6LFUlgs_2X57MHbSo9ph9qOigCuWoFGA1Rnww-LwooyAUf0Vp9rG0sdn4UgkuajQzv_w9JouWwhttps://lh4.googleusercontent.com/nnKgEKuDzahCojtsI-Hm40WYBY9IvOuwVYa89OyFLr8mK3izuUC3oMHvn0vCSrv7Ihq_BioFvNf1oQAqQ2RgGvvRX-76XDmI7JTKTXase-wd6Fahl_7wRL7EFFOKDCDL4H1pGS3INtbpV4yNEOiNCQWe now understand that a triangle's angle sum is https://lh6.googleusercontent.com/yltpi9qE6M1NBcec4MeOe8CCBun043Z645ZStPp6JPf3S4ZbZPaMRfsKM_JtG94Ju53lvtfcRZBYtZyMXAKd9lWx3oq0JuBm0o3r8x3BZoKM08RLQOCDJtJxD3zyppphTeBHffp43gz_zXJipA4wtw thanks to the triangle's angle sum condition.
Then,
https://lh5.googleusercontent.com/nuuFQO-UojjDPM2Wvec8Zk_KtSdsYOk9zlkJN8KNNrA_dKHArwpgBNotcK-42NftxrmEmq9e2k7tNNFfNUA0EiDR-0ekpgrtk6xVX319MsnFrtYMcRItc5LC8dTYJz8299BX51o-wKtHVga2PCNxmQWe'll now change https://lh3.googleusercontent.com/OnfmRTMc48LN_B9uZrTrdGOgQx613v8ZYZJ1bFBMzJWBSP81bRISFbI3SLr1sZMyCyE-ssHLbTjgzeoz4Se2fYaWPGlKFnlbJN6VEySsyb_3V2mYzT1w6fVRlGrlgTjq_Xut664uCWkidA2x_YwKBw and https://lh5.googleusercontent.com/GhAou44qzwEA3lf2SGJKiZnKWZ5C13Hd31VLM8436hMUpfTxrZ47c6atTfgeRn3lfTOlCkgvlTI7ZSLKlIMpnZC8VPmk5jAy0vm3Jh9XIJF5WorlhYEoPN0p4dp8AviREpPqWes5atdda9KzTGHLyw in the equation above to determine https://lh3.googleusercontent.com/M0vooyKanWLh1M40JoZMsDpTWJDBZ9MyOZIRfZ0gHkYktvxNLkeLYGfFuVTKq5nsgPysj3F3EuWND2a_8NJOlCWohjuYpn9h2l7wZEkwJfwI9vEKCrCdBa3mE8kKNzBNAg6wU2abr03VJmv47GDUsghttps://lh5.googleusercontent.com/cSoirtw8kpoYrsHU-wC-SnG7I8Ni6u9v_9_2djPMG_SPw5yFl43aWznqsDERGlvwRJ3xbcYc3tHefFwjFUnly_GIGWJEkAfrrrI3fugtbD8DfQKOrEXktWl2x1gIWzbVePg2JiwzrWt6LLpTZaw5qAHence, the correct option is 3) https://lh5.googleusercontent.com/12y1_pYBP8C2Nyl1kbXV3JLe14QUEzDT8ddnfFxRj-T9xB6AuuvegjNmld0Kmvb_fxqmZWR-V5D3Tpzj-Gf0T6U5dBA1EaYdiuCVoLdAYY2UQh1RosbshXMnbLk5OPwuQs-d3g5WzVVeBRb6khgxgg 
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