Question

If three angles <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> $\angle 1$, <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> $\angle 2$ and <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> $\angle 3$ are congruent and one of them is <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> ${90}^{\circ }$, then what is the sum of the other two? [2 Marks]

Answer 1

According to Euclid's postulates, all right angles are congruent with each other. [1 Mark]

So if one of the given angles is ${90}^{\circ }$, i.e., right angle and all the three angles are congruent to each other, we can say that all the angles have the measure of ${90}^{\circ }$ (using Euclid's postulate). This means the sum of the other two angles will be ${90}^{\circ }$ + ${90}^{\circ }$ = ${180}^{\circ }$. [1 Mark] <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}-->