Question

Find the unknown marked angles in the given figure:

Answer 1

From the figure

$\angle A+\angle B+\angle C={180}^{\circ }$

Substituting the values

$(m^{\circ }–5^{\circ })+{60}^{\circ }+(m^{\circ }+5^{\circ })={180}^{\circ }$

By further calculation

$m^{\circ }–5^{\circ }+{60}^{\circ }+m^{\circ }+5^{\circ }={180}^{\circ }$

$2m^{\circ }={180}^{\circ }–{60}^{\circ }={120}^{\circ }$

$m^{\circ }={120}^{\circ }/2={60}^{\circ }$

Therefore,$\angle A=m^{\circ }–5^{\circ }={60}^{\circ }–5^{\circ }={55}^{\circ }$

$\angle C=m^{\circ }+5^{\circ }={60}^{\circ }+5^{\circ }={65}^{\circ }$