The figure below shows a triangle AEB. Study and use it to answer the questions that follow. Find the value of x. Name the triangle AEB.

Tunajua kuwa jumla ya pembe za ndani za pembetatu ni $180^\circ$.
Hivyo, $\angle A + \angle E + \angle B = 180^\circ$.

Toa 20 kutoka pande zote mbili:

Gawanya kwa 6:

Jibu la Swali la 31 (a):
Thamani ya x ni: $\boxed{\frac{80}{3}}$

$\angle A = x - 10 = \frac{80}{3} - 10 = \frac{80 - 30}{3} = \frac{50}{3}^\circ \approx 16.67^\circ$
$\angle E = 3x - 10 = 3\left(\frac{80}{3}\right) - 10 = 80 - 10 = 70^\circ$
$\angle B = 2x + 40 = 2\left(\frac{80}{3}\right) + 40 = \frac{160}{3} + 40 = \frac{160 + 120}{3} = \frac{280}{3}^\circ \approx 93.33^\circ$

Kwa kuwa pembe moja ($\angle B \approx 93.33^\circ$) ni kubwa kuliko $90^\circ$, pembetatu hii ni pembetatu butu (obtuse-angled triangle).
Pia, kwa kuwa pembe zote tatu zina ukubwa tofauti, pembetatu hii pia ni pembetatu ya skelini (scalene triangle).

Jibu la Swali la 31 (b):
Pembetatu AEB ni: $\boxed{\text{Pembetatu Butu (Obtuse-angled triangle)}}$