Question

Find the Values of the Variables and the measures of the angles.

Answer 1

Answer:

The sum of the interior angle of triangle is180°

Step-by-step explanation:

(2x+4)°+(2x-9)°+x°=180

2x+4+2x-9+x=180

2x+2x+x+4-9=180

5x-5=180

5x=180-5

5x=175

$x = \frac{175}{5} \\ \\ x = 35$

$angle \ q =( 2 \times 35 + 4) \\ \\ =( 70 + 4) \\ \\ = 74$

$angle \: p =( 2 \times 35 - 9) \\ \\ = 70 - 9 \\ \\ = 61$

$angle \: r = 35$

Answer 2

Given:

Find the Values of the Variables and the measures of the angles.

Solution:

Know that the sum of the interior angle of a triangle is $\[180^\circ \]$.

$\[\begin{array}{l} \Rightarrow \left( {2x + 4} \right)^\circ + \left( {2x - 9} \right)^\circ + x^\circ = 180^\circ \\ \Rightarrow 5x - 5^\circ = 180^\circ \\ \Rightarrow x = \frac{{185^\circ }}{5}\\ \Rightarrow x = 37^\circ \end{array}\]$

Find the measure of each angle of the triangle,

Find angle Q,

$\[\begin{array}{l} \Rightarrow \angle Q = \left( {2x + 4} \right)^\circ \\ \Rightarrow \angle Q = 2 \times 37^\circ + 4^\circ \\ \Rightarrow \angle Q = 74^\circ + 4^\circ \\ \Rightarrow \angle Q = 78^\circ \end{array}\]$

Find angle P,

$\[\begin{array}{l} \Rightarrow \angle P = \left( {2x - 9} \right)^\circ \\ \Rightarrow \angle P = 2 \times 37^\circ - 9^\circ \\ \Rightarrow \angle P = 74^\circ - 9^\circ \\ \Rightarrow \angle P = 65^\circ \end{array}\]$

Find angle R,

$\[\begin{array}{l} \Rightarrow \angle R = x^\circ \\ \Rightarrow \angle R = 37^\circ \end{array}\]$

Hence, the value of the variable is $\[37^\circ \]$ and the measures of $\[\angle P,\angle Q\]$ and $\[\angle R\]$ are $\[78^\circ ,65^\circ \]$ and $\[37^\circ \]$ respectively.