# Find the measures indicated in the following circles

Find the measures indicated in the following circles

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Mike Henson

1)$$\displaystyle{2}\triangle{D}{B}{C}\ {b}{y}\ {T}{r}{i}angle\ sum\ propto{e}{r}{t}{y}$$
$$\displaystyle\angle{B}+\angle{D}+\angle{C}={180}^{{\circ}}$$
$$\displaystyle\angle{B}+{49}^{{\circ}}+{70}^{{\circ}}={180}^{{\circ}}$$
$$\displaystyle\angle{B}={61}^{{\circ}}$$
$$\displaystyle{m}\hat{{{D}{C}}}={2}\angle{B}$$
=2 x 61
$$\displaystyle={122}^{{\circ}}$$
$$\displaystyle\therefore{m}\hat{{{D}{C}}}={122}^{{\circ}}$$

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Wasither1957
2)$$\displaystyle{x}={\frac{{{80}}}{{{2}}}}$$
x = 40
y = 2 x 35
y = 70
z = 180 - y
z = 180 - 70
= 110
z = 110
x = 40
y = 70
z = 110