This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
25. Katika mchoro hapa chini, ABC ni pembetatu pacha. ADE ni pembetatu pacha yenye AD=DE. Pembe BAE ni 130^. Tafuta ukubwa wa pembe EDC. Step 1: Tumia sifa za pembetatu pacha (equilateral triangle) ABC. Kwa kuwa ABC ni pembetatu pacha, pembe zake zote ni 60^. Hivyo, BAC = 60^. Kwa kuwa D iko kwenye mstari AC, DAC ni sawa na BAC. Step 2: Kokotoa pembe DAE. Tunapewa BAE = 130^. Kutoka kwenye mchoro, BAE = BAC + DAE. Badilisha thamani zinazojulikana: 130^ = 60^ + DAE Toa 60^ kutoka pande zote mbili: DAE = 130^ - 60^ DAE = 70^ Step 3: Tumia sifa za pembetatu pacha (isosceles triangle) ADE. Tunapewa kwamba ADE ni pembetatu pacha na AD = DE. Katika pembetatu pacha, pembe zinazoelekeana na pande sawa ni sawa. Hivyo, DAE = DEA. Kwa kuwa DAE = 70^, basi DEA = 70^. Step 4: Kokotoa pembe ADE. Jumla ya pembe katika pembetatu ni 180^. Katika ADE: ADE + DAE + DEA = 180^ ADE + 70^ + 70^ = 180^ ADE + 140^ = 180^ ADE = 180^ - 140^ ADE = 40^ Step 5: Kokotoa pembe EDC. Kwa kuwa D iko kwenye mstari AC, pembe ADC ni mstari ulionyooka, hivyo ni 180^. Pembe ADE na EDC ziko kwenye mstari ulionyooka AC. Hivyo, ADE + EDC = 180^. Badilisha thamani ya ADE: 40^ + EDC = 180^ Toa 40^ kutoka pande zote mbili: EDC = 180^ - 40^ EDC = 140^ Ukubwa wa pembe EDC ni 140^. 3 done, 2 left today. You're making progress.