Question

Help!! The angle measurements in the diagram are represented by the following expressions.

Answer 1

Answer:

$\boxed{\bf \angle A=84^o}$

Step-by-step explanation:

From the given diagram, we can see that ∠B & ∠C are corresponding angles, which means that they are equal. The two angles that form a straight line are supplementary angles (the sum of two supplementary angles is 180°).

$\bf 5x+34^o+\angle C=180^o$

$\bf 5x+34^o+\angle B=180^o$

$\bf 5x+34^o+2x+76^o=180^o$

Now, let's solve for x :-

$\bf (5x+34^o)+(2x+76^o)=180^o$

$\bf (5x+2x)+(34+76)=180^o$

$\bf 7x+110=180^o$

$\bf (7x+110)-110^o=180-110^o$

$\bf 7x=70^o$

$\bf \cfrac{7x}{7} =\cfrac{70}{7}$

$\boxed{\bf x=10^o}$

Now, in order to find ∠A will substitute the value of x  into the expression:-$\bf \angle A=5x+34^o$

$\bf \angle A=5(10)+34^o$

$\bf \angle A=84^o$

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