<prompt> Katika mchoro, ikiwa angle PQR 48circ, ni kipimo gani cha angle PMN? asyukubwa 6 cm;jozi p 0, 0; jozi m dir 180 - 24; jozi n dir 180 24; jozi r 1.3 dir 24; jozi q 2 1.3 Cos 48 dir -24;leboM, m, N; leboR, r, N; leboP, p, 1.5 S; leboN, n, S; leboQ, q, SE;kuchoram--q--r--n--mzunguko;addpathticksm--p, s4;addpathticksn--p, s4;addpathticksr--p, 2, spacing0.9, s4;addpathticksr--q, 2, spacing0.9, s4;asy  <response>: Katika pembetatu PQR, tangu PRRQ, kisha angle RPQangle PQR 48circ.Kwa kuwa angle MPN na angle RPQ ni pembe kinyume, tuna angle MPN angle RPQ48circ.Katika pembetatu PMN, PMPN, hivyo angle PMN pembe PNM.Kwa hivyo, angle PMN frac12180circ - angle MPN frac12180circ - 48circ frac 12132circ66circ. 