Question

1. In the isosceles ABC shown below, Band Care base angles. If m ABC={93-73)"andZACB-3x+23), find the value of x? Then find the measure of one base angle?АBСMeasure of 1 base angle =

Answer 1

As per given by the question,

There are given that,

The measure angle is,

$m\angle ABC=(9x-73)^{\circ}$

And,

$m\angle ACB=(3x+23)^{\circ}$

Now,

From properties of isoscales triangle,

The two angles opposite to the equal sides are equal.

So,

$\angle B=\angle C$

From the given triangle;

$\begin{gathered} \angle B=\angle C \\ (9x-73)=(3x+23) \\ 9x-73-3x-23=0 \\ 6x-96 \end{gathered}$

So,

$\begin{gathered} 6x-96=0 \\ 6x=96 \\ x=\frac{96}{6} \\ =16 \end{gathered}$

Then,

For the measure first angle;

So,

Put the value of x in given angle,

$\begin{gathered} m\angle ABC=(9x-73)^{\circ} \\ =(9\times16-73) \\ =71^{\circ} \end{gathered}$

Hence, the value of x is 16 and the measure of the first base angleangle is 71 degree.