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
Step 1: Tambua aina ya poligoni na pembe zilizotolewa. Poligoni hii ina pande 5, kwa hivyo ni pentagoni. Mstari AB ni mstari mnyoofu. Pembe ya nje upande wa kushoto chini ni 70^. Pembe za ndani zilizobaki ni 2d, d, na 2d. Kutokana na alama sawa za pembe za nje chini, tunadhania pembe ya nje upande wa kulia chini pia ni 70^. Step 2: Kokotoa pembe za ndani za pentagoni. • Pembe ya ndani (chini kushoto): 180^ - 70^ = 110^. • Pembe ya ndani (juu kushoto): 2d. • Pembe ya ndani (juu katikati): d. • Pembe ya ndani (juu kulia): 2d. • Pembe ya ndani (chini kulia): 180^ - 70^ = 110^. Step 3: Tumia kanuni ya jumla ya pembe za ndani za poligoni. Kwa poligoni yenye pande n, jumla ya pembe za ndani ni (n-2) × 180^. Kwa pentagoni (n=5): Jumla ya pembe za ndani = (5-2) × 180^ = 3 × 180^ = 540^. Step 4: Tengeneza mlinganyo kwa kutumia jumla ya pembe za ndani na utatue kwa d. 110^ + 2d + d + 2d + 110^ = 540^ 220^ + 5d = 540^ 5d = 540^ - 220^ 5d = 320^ d = (320^)/(5) d = 64^ Thamani ya d ni 64^. That's 2 down. 3 left today — send the next one.