Question

50 points plus brainliest please help screenshot provided

Answer 1

Answer:

$\textsf{(a)} \quad (3x)^{\circ}+(x+14)^{\circ}=90^{\circ}$

$\textsf{(b)} \quad m \angle 1=\boxed{57}\:^{\circ}$

       $m \angle 2=\boxed{33}\:^{\circ}$

Step-by-step explanation:

From inspection of the given diagram:

• $m \angle 1=(3x)^{\circ}$

• $m \angle 2=(x+14)^{\circ}$

Part (a)

A right angle is 90° and is represented by the ∟ symbol.

To find x, equal the sum of the angles to 90° and solve for x:

$\implies m \angle 1+m\angle2=90^{\circ}$

$\implies (3x)^{\circ}+(x+14)^{\circ}=90^{\circ}$

$\implies 3x+x+14=90$

$\implies 4x+14=90$

$\implies 4x+14-14=90-14$

$\implies 4x=76$

$\implies 4x \div 4=76 \div 4$

$\implies x=19$

Part (b)

To find the degree measure of each angle, substitute the found value of x into the expression for each angle.

$\implies m \angle 1=(3 \cdot 19)^{\circ}=57^{\circ}$

$\implies m \angle 2=(19+14)^{\circ}=33^{\circ}$

Answer 2

Answer:

Equation: $\sf 3x + x + 14 = 90$

m∠1 = 57°

m∠2 = 33°

Explanation:

A right angle triangle has 90° angle measure.

Here:

m∠1 + m∠2 = 90°

(a)

Substitute given values:

(3x) + (x + 14) = 90

simplify

4x = 90 - 14

evaluate

4x = 76

divide both sides by 4

x = 19

(b)

m∠1 = 3x = 3(19) = 57°

m∠2 = x + 14 = 19 + 14 = 33°