He heights of △abc are drawn from vertices a and c. these heights intersect at point m. find m∠amc, if m∠a=70° and m∠c=80°.

150°

Step-by-step explanation:

In the given triangle ABC ∠A=70°, ∠C=80°

therefore ∠B=180-(∠A+∠C)=180-(70+80)  [sum angle property of triangle]

⇒∠B=30°

Now, heights(altitude) are drawn from vertices A and C on respective bases

they intersect at a point M. Also, we know that heights are perpendicular on the bases.

Also, point of intersection of altitudes is called orthocenter.

Now since M is orthocenter,    ∠ABC+∠AMC=180° (property of orthocenter in a triangle)

⇒30°+∠AMC=180°

⇒∠AMC=180°-30°=150°

Hence in the triangle ABC, ∠AMC=150°

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions

its kind of blurry. can you put a clearer pic?

step-by-step explanation: