Question

Suppose that QRS is isosceles with base SQ . Suppose also that =m∠R+3x47° and =m∠S+4x6° . Find the degree measure of each angle in the triangle.

Answer 1

ANSWER

$m \: < \: R = 80 \degree$

$m \: < \: S=50 \degree$
and

$m \: < \: Q = 50 \degree$



EXPLANATION

Since the triangle is an isosceles triangle, the base angles are equal.


The three interiors angles of the triangle are,

$(3x + 47) \degree,(4x + 6) \degree \: ,(4x + 6) \degree$

The sum of these three angles must equal 180°.

$(3x + 47) \degree + (4x + 6) \degree \: + (4x + 6) \degree = 180 \degree$


We group like terms to get,

$3x + 4x + 4x = 180 - 47 - 6 - 6$

This simplifies to,

$11x = 121$

We divide both sides by 11 to get,


$x = 11$


The measure of the angles are,

$(3(11)+ 47) \degree,(4(11) + 6) \degree \: ,(4(11) + 6) \degree$


$(33+ 47) \degree,(44+ 6) \degree \: ,(44 + 6) \degree$


$80\degree,50\degree \:, 50\degree$