Chapter 6.5, Problem 30PFA

To determine

To calculate the measure of angle A

Answer to Problem 30PFA

Angle A: $58°$

Explanation of Solution

Given:

In triangle ABC, angle B $=90°.$

Angle A is 6 less than twice the measure of angle C.

Concept used:

Sum of the angles of a triangle is $180°$

Calculation:

Let x be the measure of angle B and y be the measure of angle C.

Given that Angle A is 6 less than twice the measure of angle C.

  $\Rightarrow x=2y-\mathrm{6.......................}(1)$

Also, the sum of the angles of a triangle is $180°$

  $\Rightarrow x+y+B=180°$

The measurement of angle B is $90°.$

Substitute the value of B,

  $\begin{array}{l}\Rightarrow x+y+90=180\\ \Rightarrow x+y=\mathrm{90....................}(2)\end{array}$

Substitute the value of equation (1) in the above equation.

  $\begin{array}{l}\Rightarrow (2y-6)+y=90\\ \Rightarrow 3y=96\\ \Rightarrow y=32\end{array}$

Substitute the value of y in equation (2).

  $\begin{array}{l}\Rightarrow x+32+90=180\\ \Rightarrow x=58\end{array}$

Conclusion:

Therefore, the measure of angle A is $58°$ and the measure of angle C is $32°$