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.

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Huu hapa ni ufumbuzi wa swali lako:
a) Tafuta thamani ya
Step 1: Tambua pembe . Kutoka kwenye mchoro, pembe imeonyeshwa wazi kuwa . Thamani ya ni .
b) Tafuta thamani ya
Step 1: Tambua sifa za pembe tatu. Kutoka kwenye mchoro, tunaona kwamba pembe tatu ina alama mbili za vema kwenye pande zake, ikionyesha kuwa pande hizo ni sawa. Hii inamaanisha kuwa ni pembe tatu pacha (isosceles triangle).
Step 2: Tumia sifa za pembe tatu pacha. Katika pembe tatu pacha, pembe za msingi zinazokabili pande sawa ni sawa. Pembe na pembe ni pembe za msingi. Hivyo, . Kutoka sehemu (a), tunajua . Thamani ya ni .
c) Tafuta thamani ya
Step 1: Tambua uhusiano kati ya mistari sambamba na pembe. Mistari miwili ya mlalo ni sambamba (imeonyeshwa na mishale kwenye mistari). Mstari wa kushoto unaovuka mistari hii sambamba ni transversal. Pembe na pembe ni pembe mbadala za ndani (alternate interior angles).
Step 2: Tafuta thamani ya . Wakati mistari miwili ni sambamba, pembe mbadala za ndani ni sawa. Hivyo, . Kutoka sehemu (b), tunajua . Thamani ya ni .
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Huu hapa ni ufumbuzi wa swali lako: a) Tafuta thamani ya n Step 1: Tambua pembe n.
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.